exercices/3e/3G22.js

import Exercice from '../Exercice.js'
import Decimal from 'decimal.js'
import { context } from '../../modules/context.js'
import { listeQuestionsToContenu, randint, texteExposant, pgcd, fractionSimplifiee, texFractionReduite, texNombre, sp, katexPopup2, numAlpha } from '../../modules/outils.js'
export const titre = 'Connaître les effets des agrandissements/réductions sur les aires et les volumes'

/**
* Problèmes calculs d'aire et de volumes utilisant l'effet d'une réduction sur les aires et les volumes
* @author Jean-Claude Lhote
* 3G22
*/
export const uuid = '960f9'
export const ref = '3G22'
export default function AgrandissementReduction () {
  'use strict'
  Exercice.call(this) // Héritage de la classe Exercice()
  this.titre = titre
  this.consigne = ''
  this.nbQuestions = 1
  this.nbQuestionsModifiable = false
  context.isHtml ? this.spacingCorr = 3.5 : this.spacingCorr = 1.5
  context.isHtml ? this.spacing = 3 : this.spacing = 2
  this.nbCols = 1
  this.nbColsCorr = 1
  this.quatrieme = false
  this.sup = 1 //
  this.sup2 = 1
  this.pasDeVersionLatex = false

  this.nouvelleVersion = function (numeroExercice) {
    this.listeQuestions = []
    this.listeCorrections = []
    let texte, texteCorr, r, r2, h1, h2, h3, c, c2, kprime
    const pi = Decimal.acos(-1)
    //  if (context.isHtml) {
    this.typeExercice = 'MG32'
    this.dimensionsDivMg32 = [600, 700]
    let codeBase64
    let choix
    if (parseInt(this.sup) === 1) {
      choix = randint(1, 3)
    } else if (parseInt(this.sup) === 2) {
      choix = randint(4, 5)
    } else {
      choix = randint(1, 5)
    }
    switch (choix) {
      case 1: // calcul de l'aire de base, du volume d'une pyramide à base carrée. puis, calcul de la section, du volume de la petite pyramide et du volume du tronc
        c = new Decimal(randint(30, 60)).div(10)
        h1 = new Decimal(randint(12, 20)).div(2)
        h2 = new Decimal(randint(3, h1.floor().sub(1).toNumber()))
        if (this.sup2 < 3) {
          if (parseInt(this.sup2) === 1) {
            // on veut un coefficient de réduction décimal à 1 chiffre après la virgule
            while (!h2.div(h1).mul(10).eq(h2.div(h1).mul(10).round())) {
              c = new Decimal(randint(30, 60)).div(10)
              h1 = new Decimal(randint(12, 20)).div(2)
              h2 = new Decimal(randint(3, h1.floor().sub(1).toNumber()))
            }
          } else {
            // coefficient qui peut être décimal avec plus d'un chiffre ou rationnel non décimal.
            while (h2.div(h1).mul(10).eq(h2.div(h1).mul(10).round())) {
              c = new Decimal(randint(30, 60)).div(10)
              h1 = new Decimal(randint(12, 20)).div(2)
              h2 = new Decimal(randint(3, h1.floor().sub(1)))
            }
          }
        }
        codeBase64 = 'TWF0aEdyYXBoSmF2YTEuMAAAABI+TMzNAANmcmH###8BAP8BAAAAAAAAAAAFHAAAAtIAAAAAAAAAAAAAAAEAAAE1#####wAAAAEACkNDYWxjQ29uc3QA#####wACcGkAFjMuMTQxNTkyNjUzNTg5NzkzMjM4NDb#####AAAAAQAKQ0NvbnN0YW50ZUAJIftURC0Y#####wAAAAEACkNQb2ludEJhc2UA#####wAAAAAAEAAAAEAIAAAAAAAAAAAAAAAAAAAFAAFAgBQAAAAAAEBzyFHrhR64#####wAAAAEAB0NDYWxjdWwA#####wAFbWluaTEAAzAuNQAAAAE#4AAAAAAAAAAAAAMA#####wAFbWF4aTEAATMAAAABQAgAAAAAAAD#####AAAAAQAUQ0ltcGxlbWVudGF0aW9uUHJvdG8A#####wAHQ3Vyc2V1cgAAAAUAAAAFAAAAAwAAAAIAAAADAAAAAf####8AAAABABRDRHJvaXRlRGlyZWN0aW9uRml4ZQAAAAAEAQAAAAAQAAABAAEAAAABAT#wAAAAAAAA#####wAAAAEAD0NQb2ludExpZURyb2l0ZQEAAAAEAAAAAAAQAAAAwAgAAAAAAAA#8AAAAAAAAAUAAUBPAAAAAAAAAAAABf####8AAAABAAtDSG9tb3RoZXRpZQAAAAAEAAAAAf####8AAAABAApDT3BlcmF0aW9uA#####8AAAABAA9DUmVzdWx0YXRWYWxldXIAAAACAAAACAEAAAAJAAAAAgAAAAkAAAAD#####wAAAAEAC0NQb2ludEltYWdlAAAAAAQBAAAAAA0AAk8xAMAQAAAAAAAAQBAAAAAAAAAFAAAAAAYAAAAHAAAABwAAAAAEAAAAAQAAAAgDAAAACAEAAAABP#AAAAAAAAAAAAAJAAAAAgAAAAgBAAAACQAAAAMAAAAJAAAAAgAAAAoAAAAABAEAAAAADQACSTIAwAAAAAAAAABACAAAAAAAAAUAAAAABgAAAAn#####AAAAAQAIQ1NlZ21lbnQBAAAABAAAAAAAEAAAAQEBAAAAAQAAAAYAAAAGAQAAAAQAAAAAARAAAmsxAMAAAAAAAAAAQAAAAAAAAAABAAE#2973ve973wAAAAv#####AAAAAgAPQ01lc3VyZUFic2Npc3NlAQAAAAQABHpvb20AAAAIAAAACgAAAAz#####AAAAAQAPQ1ZhbGV1ckFmZmljaGVlAQAAAAQBAAAAAAAAAAAAAAAAwBgAAAAAAAAAAAAMDwAB####AAAAAQAAAAIAAAABAAAAAAAAAAAAAAAAAgAAAA0AAAADAP####8AAWMAATMAAAABQAgAAAAAAAAAAAACAP####8AAAAAAQ8AAU8AP#AAAAAAAABACAAAAAAAAAUAAUBukAAAAAAAQILsKPXCj1wAAAAFAP####8BAAAAABAAAAEAAQAAABABQACWu5jH4oIAAAACAP####8AAAAAAQ8AAk8yAQUAAUCBLAAAAAAAQHn4UeuFHrgAAAACAP####8AAAAAAQ8AAk8zAQUAAUCBJAAAAAAAQH44UeuFHrgAAAAFAP####8BAAAAABAAAAEAAQAAABMBQACWu5jH4oIAAAACAP####8AAAAAAQ8AAk80AQUAAUCBFAAAAAAAQIIcKPXCj1wAAAAFAP####8BAAAAABAAAAEAAQAAABUBQACWu5jH4oL#####AAAAAQARQ1N5bWV0cmllQ2VudHJhbGUA#####wAAABL#####AAAAAQAFQ0ZvbmMA#####wAEemVybwANYWJzKHQpPDAuMDAwMQAAAAgE#####wAAAAIACUNGb25jdGlvbgD#####AAAAAgARQ1ZhcmlhYmxlRm9ybWVsbGUAAAAAAAAAAT8aNuLrHEMtAAF0AAAABQD#####AQAAAAEQAAABAAEAAAASAD#wAAAAAAAAAAAABgD#####AAAAAAEPAAJKMgEFAADAQAAAAAAAAAAAABn#####AAAAAQAMQ1RyYW5zbGF0aW9uAP####8AAAASAAAAGgAAAAoA#####wEAAAAAEAAAAQUAAAAAEwAAABv#####AAAAAQAJQ0NlcmNsZU9BAP####8Af39#AQEAAAATAAAAHP####8AAAABABBDSW50RHJvaXRlQ2VyY2xlAP####8AAAAUAAAAHf####8AAAABABBDUG9pbnRMaWVCaXBvaW50AP####8BAAAAAA0AAkkzAQUAAQAAAB7#####AAAAAQAPQ1BvaW50TGllQ2VyY2xlAP####8AAAAAAQsAAkszAQEAAUAYJx+keskRAAAAHQAAAAsA#####wAAAAAAEAAAAQABAAAAEgAAABoAAAALAP####8AAAAAABAAAAEAAQAAABMAAAAfAAAACwD#####AAAAAAAQAAABAAEAAAATAAAAIP####8AAAACABNDTWVzdXJlQW5nbGVPcmllbnRlAP####8ACGFuZ3RoZXRhAAAAHwAAABMAAAAgAAAAAwD#####AAV0aGV0YQAIYW5ndGhldGEAAAAJAAAAJAAAAAMA#####wADeCcxAApzaW4odGhldGEpAAAAEAMAAAAJAAAAJQAAAAMA#####wADeCcyAApjb3ModGhldGEpAAAAEAQAAAAJAAAAJf####8AAAACABNDTWFycXVlQW5nbGVPcmllbnRlAP####8AfwAAAAIAAAAAQDWKaKSo2fMAAAAfAAAAEwAAACAB#####wAAAAEADENCaXNzZWN0cmljZQD#####AX8AAAAQAAABAQEAAAAfAAAAEwAAACAAAAAGAP####8BfwAAABAAAAEFAAFAebYKC41k5QAAACn#####AAAAAgAGQ0xhdGV4AP####8AfwAAAMAUAAAAAAAAwCYAAAAAAAAAAAAqEQAAAAAAAAAAAAAAAAABAAAAAAAAAAAAClx2YXJ0aGV0YSAAAAAKAP####8BAAAAABAAAAEFAAAAABoAAAAX#####wAAAAEAEkNBcmNEZUNlcmNsZURpcmVjdAD#####AH9#fwEBAAAAEgAAABoAAAAsAAAAFgD#####AAAAAAEPAAJLMgEBAAE#wCNHf8Ds#QAAAC0AAAALAP####8AAAAAABAAAAEAAQAAABIAAAAuAAAAFwD#####AAZhbmdwaGkAAAAaAAAAEgAAAC4AAAADAP####8AA3BoaQAGYW5ncGhpAAAACQAAADAAAAAHAP####8AAAAVAAAAEAQAAAAJAAAAMQAAAAMA#####wADeScxABQtY29zKHRoZXRhKSpzaW4ocGhpKQAAAAgBAAAAAQAAAAAAAAAAAAAACAIAAAAQBAAAAAkAAAAlAAAAEAMAAAAJAAAAMQAAAAMA#####wADeScyABNzaW4odGhldGEpKnNpbihwaGkpAAAACAIAAAAQAwAAAAkAAAAlAAAAEAMAAAAJAAAAMQAAABgA#####wAAAP8AAgAAAABAN1LlDbOjogAAABoAAAASAAAALgEAAAAZAP####8BAAD#ABAAAAEBAQAAABoAAAASAAAALgAAAAYA#####wEAAP8AEAAAAQUAAUB8Mk4l1syCAAAANgAAABoA#####wAAAP8AwBAAAAAAAADAFAAAAAAAAAAAADcRAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAAHXHZhcnBoaQAAAAUA#####wEAAAABEAAAAQABAAAAFQA#8AAAAAAAAAAAAAYA#####wAAAAABDwACSjQBBQABwEoAAAAAAAAAAAA5AAAAEwD#####AGZmZgABAAAAFQAAADoAAAAWAP####8BAAAAABAAAAEFAAE#8JfpunkCYQAAADsAAAAFAP####8BAAAAABAAAAEAAQAAADwAQACWu5jH4oL#####AAAAAQAQQ0ludERyb2l0ZURyb2l0ZQD#####AQAAAAAQAAABBQAAAAAWAAAAPQAAABQA#####wAAABYAAAA7AAAAFQD#####AQAAAAENAAJJNAEFAAEAAAA######wAAAAIAB0NSZXBlcmUA#####wAAAAABAQAAABUAAABAAAAAOgAAAAAAAAEAAAAAAAAAAAAAAAEAAAAAAAAAAAAAAAE#8AAAAAAAAAAAAAE#8AAAAAAAAAAAAAoA#####wEAAAAAEAAAAQUAAAAAOgAAADIAAAAHAP####8AAAA+AAAAEAQAAAAJAAAAMQAAAAoA#####wEAAAAAEAAAAQUAAAAAPAAAAEP#####AAAAAgANQ0xpZXVEZVBvaW50cwD#####AAB#fwEBAAAARAAAAGQAAAAAADwAAAAFAAAAPAAAAD0AAAA+AAAAQwAAAET#####AAAAAQAIQ1ZlY3RldXIA#####wAAAP8AEAAAAQABAAAAFQAAAEIA#####wAAAAEAEENQb2ludERhbnNSZXBlcmUA#####wEAAAAAEAAAAQUAAAAAQQAAAAkAAAAmAAAACQAAADMAAAAgAP####8BAAAAABAAAAEFAAAAAEEAAAAJAAAAJwAAAAkAAAA0AAAAHwD#####AP8AAAAQAAABAAEAAAAVAAAARwAAAAAfAP####8AAH8AABAAAAEAAQAAABUAAABIAAAAAB4A#####wBmZmYBAQAAAEcAAABkAAAAAAAgAAAABgAAACAAAAAkAAAAJQAAACYAAAAzAAAAR#####8AAAABAAxDU3VyZmFjZUxpZXUA#####wB#f38AAAAFAAAASwAAACEA#####wB#f38AAAAFAAAARQAAAAMA#####wACaDEAAjEwAAAAAUAkAAAAAAAAAAAAAwD#####AAJoMgABMwAAAAFACAAAAAAAAAAAAAMA#####wACaDMABWgxLWgyAAAACAEAAAAJAAAATgAAAAkAAABP#####wAAAAEACUNMb25ndWV1cgD#####AAAAEgAAABr#####AAAAAgAMQ0NvbW1lbnRhaXJlAP####8A#wAAAf####8QQIA8AAAAAABAdGhR64UeuAIAAAAAAAAAAAAAAAABAAAAAAAAAAAABFpPT03#####AAAAAgAJQ0NlcmNsZU9SAP####8B#wAAAAEAAAAQAAAAAT#wAAAAAAAAAAAAABQA#####wAAABEAAABTAAAAFQD#####Af8AAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAgAAAFQAAAAVAP####8B#wAAABAAAkkiAAAAAAAAAAAAQAgAAAAAAAAFAAEAAABUAAAABwD#####AAAAEAAAAAkAAAANAAAACgD#####Af8AAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAAVgAAAFf#####AAAAAQAOQ1BvaW50TGllUG9pbnQA#####wEAAAAACwACSTEAwBAAAAAAAABAEAAAAAAAAAUAAAAAWP####8AAAABAAlDRHJvaXRlQUIA#####wEAAAAADQAAAQABAAAAEAAAAFn#####AAAAAQAWQ0Ryb2l0ZVBlcnBlbmRpY3VsYWlyZQD#####AQAAAAAQAAABAAEAAAAQAAAAWgAAABMA#####wEAAAAAAQAAABAAAABZAAAAFAD#####AAAAWwAAAFwAAAAVAP####8BAAAAAAsAAkoxAMAoAAAAAAAAwBAAAAAAAAAFAAIAAABdAAAAHQD#####AICAgAEBAAAAEAAAAFkAAABeAAAAAAAAAQAAAAAAAAAAAAAAAQAAAAAAAAAAAAAAAT#wAAAAAAAAAAAAAT#wAAAAAAAAAAAAIAD#####AQAAAAAPAAFLAEAQAAAAAAAAwC4AAAAAAAAFAAAAAF8AAAABAAAAAAAAAAAAAAAQBAAAAAkAAAAxAAAAIAD#####AQAAAAAPAAFJAMAmAAAAAAAAwC4AAAAAAAAFAAAAAF8AAAAJAAAAJgAAAAkAAAAzAAAAIAD#####AQAAAAAPAAFKAEAUAAAAAAAAwCwAAAAAAAAFAAAAAF8AAAAJAAAAJwAAAAkAAAA0#####wAAAAEADUNEZW1pRHJvaXRlT0EA#####wEAAAAADQAAAQEBAAAAEAAAAGEAAAAoAP####8BAAAAAA0AAAEBAQAAABAAAABiAAAAKAD#####AQAAAAANAAABAQEAAAAQAAAAYAAAAB8A#####wH#AAAAEAAAAQABAAAAEAAAAGEAAAAAHwD#####AQB#AAAQAAABAAEAAAAQAAAAYgAAAAAfAP####8BAAD#ABAAAAEAAQAAABAAAABgAP####8AAAABABFDTWFjcm9EaXNwYXJpdGlvbgD#####AAAA#wH#####DUB+IAAAAAAAQIQQAAAAAAACAczM#wAAAAAAAAAAAAAAAQAAAAAAAAAAABMoTyxJLEosSykgaW52aXNpYmxlAAAAAAAJAAAAZAAAAGEAAABiAAAAZQAAAGgAAABgAAAAZwAAAGYAAABj#####wAAAAEAEENNYWNyb0FwcGFyaXRpb24A#####wAAAP8B#####w1AfpAAAAAAAECE4AAAAAAAAgHMzP8AAAAAAAAAAAAAAAEAAAAAAAAAAAARKE8sSSxKLEspIHZpc2libGUAAAAAAAkAAABkAAAAYQAAAGIAAABlAAAAaAAAAGAAAABnAAAAZgAAAGMA#####wAAAAEAEUNQb2ludFBhckFic2Npc3NlAP####8B#wAAABAAAkUiAAAAAAAAAAAAQAgAAAAAAAAFAAAAABAAAABhAAAACAMAAAAJAAAADwAAAAFAAAAAAAAAAAAAACUA#####wEAAAAADwABRQEFAAAAAGsAAAAMAP####8ABGFiczEAAAAQAAAAYQAAAGwAAAADAP####8AAWEABjIqYWJzMQAAAAgCAAAAAUAAAAAAAAAAAAAACQAAAG0AAAArAP####8B#wD#ABAAAAEFAAAAABAAAABiAAAACQAAAG0AAAAlAP####8BAAAAABAAAAEFAAAAAG8AAAASAP####8AAAAQAAAAcAAAAAoA#####wEAAAAADwABQgDAAAAAAAAAAEAIAAAAAAAABQAAAABsAAAAcQAAABIA#####wAAAHIAAABwAAAACgD#####AQAAAAAPAAFDAAAAAAAAAAAAQAAAAAAAAAAFAAAAAHAAAABzAAAAEgD#####AAAAcgAAAGwAAAAKAP####8BAAAAAA8AAUEAwBwAAAAAAAA#8AAAAAAAAAUAAAAAbAAAAHUAAAASAP####8AAAByAAAAdgAAAAoA#####wEAAAAADwABRADAMwAAAAAAAMAyAAAAAAAABQAAAAB0AAAAdwAAAAsA#####wAAAAAAEAAAAQEBAAAAcgAAAHQAAAALAP####8AAAAAABAAAAEBAQAAAHQAAAB4AAAACwD#####AAAAAAAQAAABAQEAAAB4AAAAdgAAAAsA#####wAAAAAAEAAAAQEBAAAAdgAAAHIAAAAXAP####8ABWFuZzEzAAAAcgAAAHYAAAB0AAAAFwD#####AAVhbmcxNAAAAHQAAAB2AAAAeAAAABcA#####wAFYW5nMTcAAAB0AAAAcgAAAHgAAAAXAP####8ABWFuZzE4AAAAeAAAAHIAAAB2AAAAFwD#####AAZhbmcxMTEAAAB4AAAAdAAAAHYAAAAXAP####8ABmFuZzExMgAAAHYAAAB0AAAAcgAAABcA#####wAGYW5nMTE1AAAAdgAAAHgAAAByAAAAFwD#####AAZhbmcxMTYAAAByAAAAeAAAAHQAAAAmAP####8BAAAAAAsAAAEBAQAAAHYAAAByAAAAJgD#####AQAAAAANAAABAQEAAAByAAAAdAAAACYA#####wEAAAAADQAAAQEBAAAAdAAAAHgAAAAmAP####8BAAAAAA0AAAEBAQAAAHgAAAB2AAAAKwD#####Af8AAAAQAAJTIgAAAAAAAAAAAEAIAAAAAAAABQAAAAAQAAAAYAAAAAkAAABOAAAAJQD#####AQAAAAAPAAFTAMAiAAAAAAAAwDIAAAAAAAAFAAAAAIkAAAAMAP####8ABWFiczE1AAAAEAAAAGAAAACKAAAAAwD#####AAFoAAVhYnMxNQAAAAkAAACLAAAACwD#####AAAAAAAQAAABAQEAAACKAAAAdgAAAAsA#####wAAAAAAEAAAAQEBAAAAigAAAHIAAAALAP####8AAAAAABAAAAEBAQAAAIoAAAB0AAAACwD#####AAAAAAAQAAABAQEAAACKAAAAeAAAABcA#####wAFYW5nMTIAAACKAAAAdgAAAHIAAAAXAP####8ABWFuZzE1AAAAeAAAAHYAAACKAAAAAwD#####AAlTQVZpc2libGUAHzEvemVybyhhbmcxMithbmcxMythbmcxNCthbmcxNSkAAAAIAwAAAAE#8AAAAAAAAP####8AAAABAA5DQXBwZWxGb25jdGlvbgAAABgAAAAIAAAAAAgAAAAACAAAAAAJAAAAkQAAAAkAAAB9AAAACQAAAH4AAAAJAAAAkgAAAAcA#####wAAAIoAAAAJAAAAkwAAAAoA#####wH#AP8AEAAAAQUAAAAAdgAAAJQAAAALAP####8BAAAAABAAAAEAAgAAAIoAAACVAAAAFwD#####AAVhbmcxNgAAAIoAAAByAAAAdAAAABcA#####wAFYW5nMTkAAAB2AAAAcgAAAIoAAAADAP####8ACVNCVmlzaWJsZQAfMS96ZXJvKGFuZzE2K2FuZzE3K2FuZzE4K2FuZzE5KQAAAAgDAAAAAT#wAAAAAAAAAAAALAAAABgAAAAIAAAAAAgAAAAACAAAAAAJAAAAlwAAAAkAAAB#AAAACQAAAIAAAAAJAAAAmAAAAAcA#####wAAAIoAAAAJAAAAmQAAAAoA#####wH#AP8AEAAAAQUAAAAAcgAAAJoAAAALAP####8BAAAAABAAAAEAAgAAAIoAAACbAAAAFwD#####AAZhbmcxMTAAAACKAAAAdAAAAHgAAAAXAP####8ABmFuZzExMwAAAHIAAAB0AAAAigAAAAMA#####wAJU0NWaXNpYmxlACMxL3plcm8oYW5nMTEwK2FuZzExMSthbmcxMTIrYW5nMTEzKQAAAAgDAAAAAT#wAAAAAAAAAAAALAAAABgAAAAIAAAAAAgAAAAACAAAAAAJAAAAnQAAAAkAAACBAAAACQAAAIIAAAAJAAAAngAAAAcA#####wAAAIoAAAAJAAAAnwAAAAoA#####wH#AP8AEAAAAQUAAAAAdAAAAKAAAAALAP####8BAAAAABAAAAEAAgAAAIoAAAChAAAAFwD#####AAZhbmcxMTQAAACKAAAAeAAAAHYAAAAXAP####8ABmFuZzExNwAAAHQAAAB4AAAAigAAAAMA#####wAJU0RWaXNpYmxlACMxL3plcm8oYW5nMTE0K2FuZzExNSthbmcxMTYrYW5nMTE3KQAAAAgDAAAAAT#wAAAAAAAAAAAALAAAABgAAAAIAAAAAAgAAAAACAAAAAAJAAAAowAAAAkAAACDAAAACQAAAIQAAAAJAAAApAAAAAcA#####wAAAIoAAAAJAAAApQAAAAoA#####wH#AP8AEAAAAQUAAAAAeAAAAKYAAAALAP####8BAAAAABAAAAEAAgAAAIoAAACnAAAAHAD#####AQAAAAANAAJXMQEFAAAAAI8AAACFAAAADAD#####AAVhYnMxMQAAAHYAAAByAAAAqf####8AAAABAA5DVGVzdEV4aXN0ZW5jZQD#####AAZUZXN0QUIAAACqAAAAAwD#####AAlBQlZpc2libGUADDEvKDEtVGVzdEFCKQAAAAgDAAAAAT#wAAAAAAAAAAAACAEAAAABP#AAAAAAAAAAAAAJAAAAqwAAAAcA#####wAAAIoAAAAJAAAArAAAAAoA#####wH#AAAAEAAAAQUAAAAAdgAAAK0AAAALAP####8BAAAAABAAAAEAAgAAAK4AAAByAAAAHAD#####AQAAAAANAAJXMgEFAAAAAJAAAACGAAAADAD#####AAVhYnMxMgAAAHIAAAB0AAAAsAAAAC0A#####wAGdGVzdEJDAAAAsQAAAAMA#####wAJQkNWaXNpYmxlAAwxLygxLXRlc3RCQykAAAAIAwAAAAE#8AAAAAAAAAAAAAgBAAAAAT#wAAAAAAAAAAAACQAAALIAAAAHAP####8AAACKAAAACQAAALMAAAAKAP####8B#wD#ABAAAAEFAAAAAHIAAAC0AAAACwD#####AQAAAAAQAAABAAIAAAC1AAAAdAAAABwA#####wEAAAAADQACVzMBBQAAAACHAAAAjQAAAAwA#####wAFYWJzMTMAAAB0AAAAeAAAALcAAAAtAP####8ABlRlc3RDRAAAALgAAAADAP####8ACUNEVmlzaWJsZQAMMS8oMS1UZXN0Q0QpAAAACAMAAAABP#AAAAAAAAAAAAAIAQAAAAE#8AAAAAAAAAAAAAkAAAC5AAAABwD#####AAAAigAAAAkAAAC6AAAACgD#####Af8A#wAQAAABBQAAAAB0AAAAuwAAAAsA#####wEAAAAAEAAAAQACAAAAvAAAAHgAAAAcAP####8BAAAAAA0AAlc0AQUAAAAAjgAAAIgAAAAMAP####8ABWFiczE0AAAAeAAAAHYAAAC+AAAALQD#####AAZUZXN0REEAAAC#AAAAAwD#####AAlEQVZpc2libGUADDEvKDEtVGVzdERBKQAAAAgDAAAAAT#wAAAAAAAAAAAACAEAAAABP#AAAAAAAAAAAAAJAAAAwAAAAAcA#####wAAAIoAAAAJAAAAwQAAAAoA#####wH#AP8AEAAAAQUAAAAAeAAAAMIAAAALAP####8BAAAAABAAAAEAAgAAAMMAAAB2#####wAAAAEADkNPYmpldER1cGxpcXVlAP####8AAAAAAAAArwAAAC4A#####wAAAAAAAAC2AAAALgD#####AAAAAAAAAJYAAAAuAP####8AAAAAAAAAnAAAAC4A#####wAAAAAAAACiAAAALgD#####AAAAAAAAAL0AAAAuAP####8AAAAAAAAAxAAAAC4A#####wAAAAAAAACoAAAAKwD#####AAAAAAEQAAJPJwBACAAAAAAAAEAAAAAAAAAABQAAAAAQAAAAYAAAAAkAAABQAAAACwD#####Af8AAAAQAAABAAEAAACJAAAAawAAAAcA#####wAAAIkAAAAJAAAAkwAAAAcA#####wAAAIkAAAAJAAAArAAAAAcA#####wAAAIkAAAAJAAAAswAAAAcA#####wAAAIkAAAAJAAAAugAAAAcA#####wAAAIkAAAAJAAAAwQAAAAsA#####wAAAAAAEAAAAQEBAAAAEAAAAHT#####AAAAAQAQQ0Ryb2l0ZVBhcmFsbGVsZQD#####Af8AAAAQAAABAQEAAADNAAAA1AAAAAsA#####wH#AAAAEAAAAQEBAAAAEAAAAHIAAAAvAP####8B#wAAABAAAAEBAQAAAM0AAADWAAAABwD#####AAAAiQAAAAkAAACZAAAABwD#####AAAAiQAAAAkAAACfAAAABwD#####AAAAiQAAAAkAAACl#####wAAAAEACUNQb2x5Z29uZQD#####ANjY2AEBAAAABQAAAHYAAAByAAAAdAAAAHgAAAB2#####wAAAAEAEENTdXJmYWNlUG9seWdvbmUA#####wB#f38AAAAFAAAA2wAAAAcA#####wAAABAAAAABP#B64UeuFHsAAAAKAP####8B#wAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAACKAAAA3QAAACMA#####wAAAAAAwDQAAAAAAADAJgAAAAAAAAAAAN4QAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAADI0dTAAAAFAD#####AAAA1AAAAFMAAAAVAP####8BAAAAABAAAUYAAAAAAAAAAABACAAAAAAAAAUAAQAAAOAAAAAVAP####8AAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQACAAAA4AAAACsA#####wEAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAABAAAADhAAAAAT#gAAAAAAAAAAAABwD#####AAAAEAAAAAgDAAAAEAQAAAAJAAAAMQAAAAFAAAAAAAAAAAAAAAsA#####wAAAAAAEAAAAQEBAAAAEAAAAOMAAAASAP####8AAAAQAAAA4wAAAAoA#####wAAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAAM0AAADmAAAACwD#####AAAAAAAQAAABAQEAAADNAAAA5wAAAAsA#####wAAAAAAEAAAAQEBAAAAeAAAAHIAAAALAP####8AAAAAABAAAAEBAQAAAHYAAAB0AAAAFAD#####AAAAZQAAAFMAAAAVAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQABAAAA6wAAABUA#####wAAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAIAAADrAAAABwD#####AAAAEAAAAAgDAAAAEAAAAAAQBAAAAAkAAAAxAAAAAUAAAAAAAAAAAAAACgD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAA7AAAAO4AAAASAP####8AAAAQAAAA7wAAAAoA#####wEAAAAAEAAAAEAIAAAAAAAAAAAAAAAAAAAFAAAAAOMAAADwAAAACwD#####AAAAAAAQAAABAQEAAADvAAAAEAAAAAsA#####wAAAAAAEAAAAQEBAAAA4wAAAPEAAAALAP####8AAAAAABAAAAEBAQAAAPEAAADvAAAAMAD#####AAAAAAEBAAAABQAAAO8AAAAQAAAA4wAAAPEAAADvAAAACgD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAAzQAAAPAAAAASAP####8AAADNAAAA9gAAAAoA#####wEAAAAAEAAAAEAIAAAAAAAAAAAAAAAAAAAFAAAAAOcAAAD3AAAACwD#####AAAAAAAQAAABAQEAAAD2AAAAzQAAAAsA#####wAAAAAAEAAAAQEBAAAA5wAAAPgAAAALAP####8AAAAAABAAAAEBAQAAAPgAAAD2AAAAMAD#####AAAAAAEBAAAABQAAAPYAAADNAAAA5wAAAPgAAAD2AAAABwD#####AAAAiQAAAAgDAAAACQAAAE8AAAAJAAAATgAAAAoA#####wEAAAAAEAACQycAQCQAAAAAAADAMAAAAAAAAAUAAAAAdAAAAP0AAAAHAP####8AAACJAAAACAMAAAAJAAAATwAAAAkAAABOAAAACgD#####AQAAAAAQAAJCJwBAJAAAAAAAAMAAAAAAAAAABQAAAAByAAAA#wAAAAoA#####wEAAAAAEAACQScAwDgAAAAAAAC#8AAAAAAAAAUAAAAAdgAAAP8AAAAKAP####8BAAAAABAAAkQnAMA6AAAAAAAAwCYAAAAAAAAFAAAAAHgAAAD#AAAAMAD#####AAAAAAEBAAAABQAAAQEAAAEAAAAA#gAAAQIAAAEBAAAAMQD#####AP8AAAAAAAUAAAEDAAAACwD#####AP8AAAAQAAABAQEAAAEBAAAA#gAAAAsA#####wD#AAAAEAAAAQEBAAABAgAAAQAAAAAKAP####8B#wAAABAAAkEyAAAAAAAAAAAAQAgAAAAAAAAFAAAAAQEAAADQAAAACgD#####Af8AAAAQAAJCMgAAAAAAAAAAAEAIAAAAAAAABQAAAAEAAAAA0AAAAAsA#####wD#AAAAEAAAAQACAAABBwAAAQgAAAAKAP####8B#wAAABAAAkIzAAAAAAAAAAAAQAgAAAAAAAAFAAAAAQAAAADRAAAACgD#####Af8AAAAQAAJDMwAAAAAAAAAAAEAIAAAAAAAABQAAAAD+AAAA0QAAAAsA#####wD#AAAAEAAAAQACAAABCgAAAQsAAAAKAP####8B#wAAABAAAkM0AAAAAAAAAAAAQAgAAAAAAAAFAAAAAP4AAADSAAAACgD#####Af8AAAAQAAJENAAAAAAAAAAAAEAIAAAAAAAABQAAAAECAAAA0gAAAAsA#####wD#AAAAEAAAAQACAAABDQAAAQ4AAAAKAP####8B#wAAABAAAkQzAAAAAAAAAAAAQAgAAAAAAAAFAAAAAQIAAADTAAAACgD#####Af8AAAAQAAJBMwAAAAAAAAAAAEAIAAAAAAAABQAAAAEBAAAA0wAAAAsA#####wD#AAAAEAAAAQACAAABEAAAAREAAAArAP####8B#wAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAAAQAAAAdgAAAAE#8ZmZmZmZmgAAACsA#####wH#AAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAABAAAAB0AAAAAT#xmZmZmZmaAAAAKwD#####Af8AAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAAEAAAAHIAAAABP#GZmZmZmZoAAAArAP####8B#wAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAAAQAAAAeAAAAAE#8ZmZmZmZmgAAACMA#####wAAAAAAwBgAAAAAAADAIgAAAAAAAAAAARMQAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAABQQAAACMA#####wAAAAAAwBgAAAAAAADAHAAAAAAAAAAAARUQAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAABQgAAACMA#####wAAAAAAwBwAAAAAAADAIAAAAAAAAAAAARQQAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAABQwAAACMA#####wAAAAAAwBgAAAAAAADAJAAAAAAAAAAAARYQAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAABRAAAACsA#####wEAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAAM0AAAEBAAAAAT#0zMzMzMzNAAAAKwD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAAzQAAAQAAAAABP#TMzMzMzM0AAAArAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAADNAAABAgAAAAE#9MzMzMzMzQAAACsA#####wEAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAAM0AAAD+AAAAAT#0zMzMzMzNAAAAIwD#####AAAAAADAFAAAAAAAAMAmAAAAAAAAAAABGxAAAAAAAAAAAAAAAAAAAQAAAAAAAAAAAAJBJwAAACMA#####wAAAAAAwAgAAAAAAADAIAAAAAAAAAAAARwQAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAACQicAAAAjAP####8AAAAAAMAYAAAAAAAAwCAAAAAAAAAAAAEeEAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAkMnAAAAIwD#####AAAAAADAHAAAAAAAAMAiAAAAAAAAAAABHRAAAAAAAAAAAAAAAAAAAQAAAAAAAAAAAAJEJwAAACsA#####wEAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAAIkAAADNAAAAAT#zMzMzMzMzAAAADgD#####AAAAzQAAAAoA#####wEAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAAOcAAAEkAAAAEgD#####AAAAzQAAASMAAAAKAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAAElAAABJgAAACMA#####wAAAAAAwAgAAAAAAADAKgAAAAAAAAAAAScQAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAAEI0dPJwAAAA4A#####wAAABAAAAAKAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAADjAAABKQAAAAoA#####wEAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAASoAAAEmAAAAIwD#####AAAAAADAEAAAAAAAAMAxAAAAAAAAAAABKxAAAAAAAAAAAAAAAAAAAQAAAAAAAAAAAAMjR0######AAAAAQAHQ01pbGlldQD#####AQAAAAAPAAFHAAAAAAAAAAAAQAgAAAAAAAAFAAAAAHQAAAByAAAAKwD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAAEAAAAS0AAAABP#MzMzMzMzMAAAANAP####8AAAAAAQAAAS4SAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAAAAAACAAAADwAAADIA#####wEAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAAM0AAACJAAAAMgD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAAEAAAAM0AAAANAP####8AAAAAAMAqAAAAAAAAwCIAAAAAAAAAAAExEAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAgAAAFAAAAANAP####8AAAAAAMAmAAAAAAAAwBgAAAAAAAAAAAEwEAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAgAAAE8AAAALAP####8AAAAAABAAAAEBAQAAABAAAACKAAAAUf##########'
        if (!context.isHtml) {
          texte = '\\begin{minipage}{0.65 \\linewidth} \n\t'
        } else {
          texte = ''
        }
        texte += `SABCD est une pyramide à base carrée de hauteur $SO${sp()}=${sp()}${texNombre(h1, 1)}${sp()}$cm et de côté de base $${texNombre(c, 1)}${sp()}$cm.<br>`
        texte += ` Le point O' est situé sur la hauteur [SO] à ${texNombre(h2, 0)}${sp()}cm de S.`
        texte += '<br>Un plan parallèle à la face ABCD passant par O\' coupe la pyramide en formant la section A\'B\'C\'D\'.<br>'
        if (!context.isHtml) {
          texte += 'La figure n\'est pas en vraie grandeur.<br>'
        }
        texte += numAlpha(0) + ' Calculer l\'' + katexPopup2(numeroExercice, 1, 'aire de base de la pyramide', 'Formule : Aire d\'un carré de côté c', `$Aire=\\text{c}$${texteExposant(2)}`) + '.<br>'
        texte += numAlpha(1) + ' Calculer le ' + katexPopup2(numeroExercice + 5, 1, 'volume de la pyramide', 'Formule : volume d\'une pyramide d\'aire de base $B$ et de hauteur h', '$Volume= \\dfrac{B \\times \\text{h}}{3}$') + ' SABCD.<br>'
        texte += numAlpha(2) + ' En déduire l\'aire de la ' + katexPopup2(numeroExercice + 10, 1, 'section', 'Définition : section plane d\'un solide', `La section d'un solide par un plan est une figure plane.<br>Dans le cas d'une section d'une pyramide par un plan parallèle à sa base, cette section est un polygone qui est une réduction de la base.<br>Dans une réduction de coefficient k, les aires sont multipliées par k${texteExposant(2)} et les volumes sont multipliés par k${texteExposant(3)}.`) + ` A'B'C'D' sachant que SO'${sp()}=${sp()}${texNombre(h2, 0)}${sp()}cm.<br>`
        texte += numAlpha(3) + ' Calculer le volume de la pyramide SA\'B\'C\'D\'.<br>'
        texte += numAlpha(4) + ' Calculer le volume du tronc de la pyramide (partie de la pyramide située entre la base et la section).'
        if (context.isHtml) {
          texte += '<br>Le point O peut être déplacé et on peut changer l\'angle de vue &#x3C6; '
        } else {
          texte += `\n\t \\end{minipage} \n\t \\begin{minipage}{0.35 \\linewidth} \n\t \\begin{tikzpicture}[scale=0.8] \n\t
          \\definecolor{hhhhhh}{rgb}{0,0,0}
          \\definecolor{phphph}{rgb}{0.5,0.5,0.5}
          \\definecolor{dpdpdp}{rgb}{0.85,0.85,0.85}
          \\definecolor{ofofof}{rgb}{0.5,0.5,0.5}
          \\definecolor{ffhhhh}{rgb}{1,0,0}
          \\clip (9.38,0) rectangle (0,14.47);
          \\fill[color=black] (4.578,2.328) circle (0.063);
          \\draw [color=black , dotted, line width = 0.4](6.773,0.916)--(8.236,3.174);
          \\draw [color=black , dotted, line width = 0.4](8.236,3.174)--(2.384,3.739);
          \\draw [color=black , dotted, line width = 0.4](2.384,3.739)--(0.921,1.481);
          \\draw [color=black , dotted, line width = 0.4](0.921,1.481)--(6.773,0.916);
          \\draw [color=black , dotted, line width = 0.4](4.578,13.458)--(0.921,1.481);
          \\draw [color=black , dotted, line width = 0.4](4.578,13.458)--(6.773,0.916);
          \\draw [color=black , dotted, line width = 0.4](4.578,13.458)--(8.236,3.174);
          \\draw [color=black , dotted, line width = 0.4](4.578,13.458)--(2.384,3.739);
          \\draw [color=black , line width = 0.8](0.921,1.481)--(6.773,0.916);
          \\draw [color=black , line width = 0.8](6.773,0.916)--(8.236,3.174);
          \\draw [color=black , line width = 0.8](4.578,13.458)--(0.921,1.481);
          \\draw [color=black , line width = 0.8](4.578,13.458)--(6.773,0.916);
          \\draw [color=black , line width = 0.8](4.578,13.458)--(8.236,3.174);
          \\fill[color=black] (4.578,6.501) circle (0.063);
          \\draw [color=black , dotted, line width = 0.4](4.578,2.328)--(8.236,3.174);
          \\draw [color=dpdpdp , dotted, line width = 0.4](0.921,1.481)--(6.773,0.916)--(8.236,3.174)--(2.384,3.739)--(0.921,1.481)--cycle;
          \\fill [color = ofofof, opacity = 0.2](0.921,1.481)--(6.773,0.916)--(8.236,3.174)--(2.384,3.739)--(0.921,1.481)--cycle;
          \\node at (3.891, 14.198) [align=left,below right ,black,,font= \\sf \\fontsize {0.469cm} {0.586cm} \\selectfont] {\\textbf{S}};
          \\draw [color=black , dotted, line width = 0.4](4.578,2.328)--(5.065,2.44);
          \\fill[color=black] (5.065,6.614) circle (0.063);
          \\draw [color=black , dotted, line width = 0.4](4.578,6.501)--(5.065,6.614);
          \\draw [color=black , dotted, line width = 0.4](2.384,3.739)--(6.773,0.916);
          \\draw [color=black , dotted, line width = 0.4](0.921,1.481)--(8.236,3.174);
          \\draw [color=black , dotted, line width = 0.4](4.578,2.789)--(4.578,2.328);
          \\draw [color=black , dotted, line width = 0.4](5.065,2.44)--(5.065,2.902);
          \\draw [color=black , dotted, line width = 0.4](5.065,2.902)--(4.578,2.789);
          \\draw [color=black , dotted, line width = 0.4](4.578,2.789)--(4.578,2.328)--(5.065,2.44)--(5.065,2.902)--(4.578,2.789)--cycle;
          \\draw [color=black , dotted, line width = 0.4](4.578,6.963)--(4.578,6.501);
          \\draw [color=black , dotted, line width = 0.4](5.065,6.614)--(5.065,7.075);
          \\draw [color=black , dotted, line width = 0.4](5.065,7.075)--(4.578,6.963);
          \\draw [color=black , dotted, line width = 0.4](4.578,6.963)--(4.578,6.501)--(5.065,6.614)--(5.065,7.075)--(4.578,6.963)--cycle;
          \\draw [color=black , dotted, line width = 0.4](2.292,5.972)--(5.95,5.619)--(6.864,7.031)--(3.207,7.383)--(2.292,5.972)--cycle;
          \\fill [color = ffhhhh, opacity = 0.2](2.292,5.972)--(5.95,5.619)--(6.864,7.031)--(3.207,7.383)--(2.292,5.972)--cycle;
          \\draw [color=ffhhhh , dotted, line width = 0.4](2.292,5.972)--(6.864,7.031);
          \\draw [color=ffhhhh , dotted, line width = 0.4](3.207,7.383)--(5.95,5.619);
          \\draw [color=ffhhhh , line width = 0.8](2.292,5.972)--(5.95,5.619);
          \\draw [color=ffhhhh , line width = 0.8](5.95,5.619)--(6.864,7.031);
          \\node at (0.305, 1.74) [align=left,below right ,black,,font= \\sf \\fontsize {0.469cm} {0.586cm} \\selectfont] {A};
          \\node at (6.742, 1.057) [align=left,below right ,black,,font= \\sf \\fontsize {0.469cm} {0.586cm} \\selectfont] {B};
          \\node at (8.32, 3.571) [align=left,below right ,black,,font= \\sf \\fontsize {0.469cm} {0.586cm} \\selectfont] {C};
          \\node at (1.914, 4.255) [align=left,below right ,black,,font= \\sf \\fontsize {0.469cm} {0.586cm} \\selectfont] {D};
          \\node at (1.544, 6.407) [align=left,below right ,black,,font= \\sf \\fontsize {0.469cm} {0.586cm} \\selectfont] {A'};
          \\node at (6.205, 5.667) [align=left,below right ,black,,font= \\sf \\fontsize {0.469cm} {0.586cm} \\selectfont] {B'};
          \\node at (7.112, 7.564) [align=left,below right ,black,,font= \\sf \\fontsize {0.469cm} {0.586cm} \\selectfont] {C'};
          \\node at (2.201, 7.992) [align=left,below right ,black,,font= \\sf \\fontsize {0.469cm} {0.586cm} \\selectfont] {D'};
          \\node at (3.935, 5.466) [align=left,below right ,black,,font= \\sf \\fontsize {0.469cm} {0.586cm} \\selectfont] {\\textbf{O'}};
          \\node at (4.247, 2.292) [align=left,below right ,black,,font= \\sf \\fontsize {0.469cm} {0.586cm} \\selectfont] {\\textbf{O}};
          \\draw [color=black , dotted, line width = 0.4](4.578,2.328)--(4.578,13.458);
          \\end{tikzpicture} \n\t \\end{minipage}`
        }
        texteCorr = numAlpha(0) + ` L'aire de base de la pyramide est : $${texNombre(c, 1)}^2$ cm${texteExposant(2)} $= ${texNombre(c * c)}$ cm${texteExposant(2)}.<br>`
        texteCorr += numAlpha(1) + ` Le volume de la pyramide est : $\\dfrac{A_\\text{base} \\times \\text{hauteur}}{3}$ cm${texteExposant(3)} $= \\dfrac{${texNombre(c * c)}\\times ${texNombre(h1, 1)}}{3}$ cm${texteExposant(3)} $\\approx ${texNombre(c.mul(c).mul(h1).div(3), 3)}$ cm${texteExposant(3)}.<br>`
        texteCorr += numAlpha(2) + ` La section est une réduction de la base de coefficient $\\dfrac{${texNombre(h2, 0)}}{${texNombre(h1, 1)}}`
        if (!Number.isInteger(h1) || pgcd(h2, h1) > 1) {
          texteCorr += `=${texFractionReduite(h2.mul(10), h1.mul(10))}$.<br>`
        } else {
          texteCorr += '.$<br>'
        }
        texteCorr += `Dans une réduction de coefficient k, les aires sont multipliés par k${texteExposant(2)}.<br>`
        texteCorr += `Donc son aire est $\\left(${texFractionReduite(h2.mul(10), h1.mul(10))}\\right)^2 \\times ${texNombre(c * c)}$ cm${texteExposant(2)} $=${texFractionReduite(h2.mul(c).mul(10).pow(2), h1.mul(10).pow(2))}$ cm${texteExposant(2)} $\\approx ${texNombre(h2.mul(c).div(h1).pow(2), 2)}$ cm${texteExposant(2)}.<br>`
        texteCorr += numAlpha(3) + ` Dans une réduction de coefficient k, les volumes sont multipliés par k ${texteExposant(3)}.<br>`
        texteCorr += `Donc le volume de la pyramide SA'B'C'D' est : $\\left(${texFractionReduite(h2.mul(10), h1.mul(10))}\\right)^3 \\times \\dfrac{${texNombre(c * c * h1)}}{3}$ cm${texteExposant(3)} $\\approx ${texNombre(h2.pow(3).mul(c.pow(2)).div(h1.pow(2)).div(3), 3)}$ cm${texteExposant(3)}.<br>`
        texteCorr += numAlpha(4) + ' Le volume du tronc de la pyramide est : '
        texteCorr += `$V_\\text{SABCD} - V_\\text{SA'B'C'D'}$<br>Soit : <br>$${texNombre(h1.mul(c).mul(c).div(3), 3)}$ cm${texteExposant(3)}$ - ${texNombre(h2.pow(3).mul(c).mul(c).div(h1.pow(2)).div(3), 3)}$ cm${texteExposant(3)}$ \\approx ${texNombre(h1.sub(h2.pow(3).div(h1.pow(2))).mul(c.pow(2)).div(3), 2)}$ cm${texteExposant(3)}.<br>`
        texteCorr += `Ce qui représente $${texFractionReduite(h1.pow(3).sub(h2.pow(3)).mul(1000), h1.pow(3).mul(1000))}$ du volume de SABCD.`

        this.MG32codeBase64 = codeBase64
        this.mg32init = (mtg32App, idDoc) => {
          mtg32App.giveFormula2(idDoc, 'c', c.toString())
          mtg32App.giveFormula2(idDoc, 'h1', h1.toString())
          mtg32App.giveFormula2(idDoc, 'h2', h2.toString())
          // le 2e argument à true sert à recalculer les rand() éventuels contenus dans les formules,
          // à priori inutile ici (car on initialise une figure), mais ça mange pas de pain
          mtg32App.calculate(idDoc, true)
          return mtg32App.display(idDoc)
        }
        break
      case 2: // calcul de l'aire de base, du volume d'un cône. puis, calcul de la section, du volume du cône réduit et du volume du tronc
        r = new Decimal(randint(12, 35)).div(10)
        h1 = new Decimal(randint(12, 20)).div(2)
        h2 = new Decimal(3, Math.floor(h1) - 1)
        if (this.sup2 < 3) {
          if (parseInt(this.sup2) === 1) { // coefficient de réduction décimal
            while (!h2.div(h1).mul(10).eq(h2.div(h1).mul(10).round())) {
              r = new Decimal(randint(12, 35)).div(10)
              h1 = new Decimal(randint(12, 20)).div(2)
              h2 = new Decimal(3, Math.floor(h1) - 1)
            }
          } else { // coefficient de réduction rationnel
            while (h2.div(h1).mul(10).eq(h2.div(h1).mul(10).round())) {
              r = new Decimal(randint(12, 35)).div(10)
              h1 = new Decimal(randint(12, 20)).div(2)
              h2 = new Decimal(3, Math.floor(h1) - 1)
            }
          }
        }
        codeBase64 = 'TWF0aEdyYXBoSmF2YTEuMAAAABI+TMzNAANmcmH###8BAP8BAAAAAAAAAAAFHAAAAtIAAAAAAAAAAAAAAAAAAAET#####wAAAAEACkNDYWxjQ29uc3QA#####wACcGkAFjMuMTQxNTkyNjUzNTg5NzkzMjM4NDb#####AAAAAQAKQ0NvbnN0YW50ZUAJIftURC0Y#####wAAAAEAD0NWYXJpYWJsZUJvcm5lZQD#####AANhbmc#6SH7VEQtGAAAAAAAAAAAQBkh+1RELRg#qZmZmZmZmgAAATAABDIqcGkABDAuMDX#####AAAAAQAKQ1BvaW50QmFzZQD#####AQAAAAAQAAAAQAgAAAAAAAAAAAAAAAAAAAUAAUB#eAAAAAAAQHqoUeuFHrj#####AAAAAQAHQ0NhbGN1bAD#####AAVtaW5pMQADMC4yAAAAAT#JmZmZmZmaAAAABAD#####AAVtYXhpMQABMgAAAAFAAAAAAAAAAP####8AAAABABRDSW1wbGVtZW50YXRpb25Qcm90bwD#####AAdDdXJzZXVyAAAABQAAAAUAAAADAAAAAwAAAAQAAAAC#####wAAAAEAFENEcm9pdGVEaXJlY3Rpb25GaXhlAAAAAAUBAAAAABAAAAEAAQAAAAIBP#AAAAAAAAD#####AAAAAQAPQ1BvaW50TGllRHJvaXRlAQAAAAUBAAAAABAAAADACAAAAAAAAD#wAAAAAAAABQABQEuAAAAAAAAAAAAG#####wAAAAEAC0NIb21vdGhldGllAAAAAAUAAAAC#####wAAAAEACkNPcGVyYXRpb24D#####wAAAAEAD0NSZXN1bHRhdFZhbGV1cgAAAAMAAAAJAQAAAAoAAAADAAAACgAAAAT#####AAAAAQALQ1BvaW50SW1hZ2UAAAAABQEAAAAADQACTzEAwBAAAAAAAABAEAAAAAAAAAUAAAAABwAAAAgAAAAIAAAAAAUAAAACAAAACQMAAAAJAQAAAAE#8AAAAAAAAAAAAAoAAAADAAAACQEAAAAKAAAABAAAAAoAAAADAAAACwAAAAAFAQAAAAANAAJJNQDAAAAAAAAAAEAIAAAAAAAABQAAAAAHAAAACv####8AAAABAAhDU2VnbWVudAEAAAAFAQAAAAAQAAABAQEAAAACAAAABwAAAAcBAAAABQEAAAABEAACazEAwAAAAAAAAABAAAAAAAAAAAEAAT#ZmZmZmZmaAAAADP####8AAAACAA9DTWVzdXJlQWJzY2lzc2UBAAAABQAEem9vbQAAAAkAAAALAAAADf####8AAAABAA9DVmFsZXVyQWZmaWNoZWUBAAAABQEAAAAAAAAAAAAAAADAGAAAAAAAAAAAAA0PAAH###8AAAABAAAAAgAAAAEAAAAAAAAAAAAAAAACAAAADgAAAAMA#####wH#AAAAEAABWgAAAAAAAAAAAEAIAAAAAAAABQABQHmoAAAAAABAd2hR64UeuAAAAAgA#####wAAABAAAAAKAAAADgAAAAYA#####wH#AAABEAAAAQEBAAAAEAA#8AAAAAAAAAAAAAcA#####wH#AAAAEAABTQAAAAAAAAAAAEAIAAAAAAAABQABwEgAAAAAAAAAAAASAAAACwD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAAEwAAABEAAAADAP####8BAAAAAQ8AAk8yAQUAAUCA3AAAAAAAQICEKPXCj1wAAAAGAP####8BAAAAARAAAAEAAQAAABUAP#AAAAAAAAAAAAAHAP####8BAAAAAQ8AAkoyAQUAAMBAAAAAAAAAAAAAFv####8AAAABAAlDTG9uZ3VldXIA#####wAAABUAAAAXAAAAAwD#####AAAAAAAPAAFPAMAyAAAAAAAAwCgAAAAAAAAFAAFAYnAAAAAAAEB4mFHrhR64AAAABgD#####AQAAAAAQAAABAAEAAAAZAUAD6BRQ79ycAAAABwD#####Af8AAAAQAAJJIgAAAAAAAAAAAEAIAAAAAAAABQABQDF7TwMpFiAAAAAaAAAABAD#####AAJoMQACMTAAAAABQCQAAAAAAAAAAAAEAP####8AAmgyAAE0AAAAAUAQAAAAAAAAAAAABAD#####AAFyAAMzLjUAAAABQAwAAAAAAAD#####AAAAAQARQ1N5bWV0cmllQ2VudHJhbGUA#####wAAABUAAAADAP####8BAAAAAQ8AAk8zAQUAAUCSQgAAAAAAQHe4UeuFHrcAAAAGAP####8BAAAAABAAAAEAAQAAACABQAPoFFDv3JwAAAADAP####8BAAAAAQsAAk80AQUAAUCSVgAAAAAAQH5YUeuFHrgAAAAGAP####8BAAAAABAAAAEAAQAAACIBQAPoFFDv3JwAAAAQAP####8AAAAZAAAACwD#####AQB#AAALAAJXNADANQAAAAAAAMAUAAAAAAAABQAAAAAXAAAAH#####8AAAABAAxDVHJhbnNsYXRpb24A#####wAAABUAAAAXAAAACwD#####AQAAAAALAAJXNwBAAAAAAAAAAAAAAAAAAAAABQAAAAAgAAAAJv####8AAAABAAlDQ2VyY2xlT0EA#####wF#f38BAQAAACAAAAAn#####wAAAAEAEENJbnREcm9pdGVDZXJjbGUA#####wAAACEAAAAo#####wAAAAEAEENQb2ludExpZUJpcG9pbnQA#####wEAAAAADQACSTMBBQABAAAAKf####8AAAABAA9DUG9pbnRMaWVDZXJjbGUA#####wEAAAABCwACSzMBAQABQBX9VSbZZwcAAAAo#####wAAAAIAE0NNZXN1cmVBbmdsZU9yaWVudGUA#####wAIYW5ndGhldGEAAAAqAAAAIAAAACsAAAAEAP####8ABXRoZXRhAAhhbmd0aGV0YQAAAAoAAAAsAAAABAD#####AAN4JzEACnNpbih0aGV0YSn#####AAAAAgAJQ0ZvbmN0aW9uAwAAAAoAAAAtAAAABAD#####AAN4JzIACmNvcyh0aGV0YSkAAAAXBAAAAAoAAAAtAAAAFQD#####AQAAAAALAAJXMQDAAAAAAAAAAEAAAAAAAAAABQABQBNc46k8Cu8AAAAoAAAAFgD#####AAVhbmdsZQAAACoAAAAgAAAAMP####8AAAABABJDQXJjRGVDZXJjbGVEaXJlY3QA#####wF#f38BAQAAABUAAAAXAAAAJQAAABUA#####wEAAAABCwACSzIBAQABP8B#LK14eQYAAAAyAAAAFgD#####AAZhbmdwaGkAAAAXAAAAFQAAADMAAAAEAP####8AA3BoaQAGYW5ncGhpAAAACgAAADQAAAAEAP####8AA3knMQAULWNvcyh0aGV0YSkqc2luKHBoaSkAAAAJAQAAAAEAAAAAAAAAAAAAAAkCAAAAFwQAAAAKAAAALQAAABcDAAAACgAAADUAAAAEAP####8AA3knMgATc2luKHRoZXRhKSpzaW4ocGhpKQAAAAkCAAAAFwMAAAAKAAAALQAAABcDAAAACgAAADX#####AAAAAQAXQ01lc3VyZUFuZ2xlR2VvbWV0cmlxdWUA#####wAAABcAAAAVAAAAJQAAAAQA#####wAEcGxhdAAGSjJPMlc0AAAACgAAADgAAAAEAP####8ABWRyb2l0AAZwbGF0LzIAAAAJAwAAAAoAAAA5AAAAAUAAAAAAAAAAAAAADAD#####AQAAAAAQAAABAAEAAAAVAAAAFwAAAAwA#####wEAAAAAEAAAAQABAAAAIAAAACoAAAAMAP####8BAAAAABAAAAEAAQAAACAAAAAr#####wAAAAIAE0NNYXJxdWVBbmdsZU9yaWVudGUA#####wF#AAAAAgAAAABAOLK7zEtlnQAAACoAAAAgAAAAKwH#####AAAAAQAMQ0Jpc3NlY3RyaWNlAP####8BfwAAABAAAAEBAQAAACoAAAAgAAAAKwAAAAcA#####wF#AAAAEAAAAQUAAUB5tgoLjWTlAAAAP#####8AAAACAAZDTGF0ZXgA#####wF#AAAAwBQAAAAAAADAJgAAAAAAAAAAAEARAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAAKXHZhcnRoZXRhIAAAAAwA#####wEAAAAAEAAAAQABAAAAFQAAADMAAAAIAP####8AAAAiAAAAFwQAAAAKAAAANQAAABoA#####wEAAP8AAgAAAABAN1LlDbOjogAAABcAAAAVAAAAMwEAAAAbAP####8BAAD#ABAAAAEBAQAAABcAAAAVAAAAMwAAAAcA#####wEAAP8AEAAAAQUAAUB3uGBZxKE1AAAARQAAABwA#####wEAAP8AAAAAAAAAAADAFAAAAAAAAAAAAEYRAAAAAAABAAAAAQAAAAEAAAAAAAAAAAAHXHZhcnBoaQAAAAQA#####wABawAIc2luKHBoaSkAAAAXAwAAAAoAAAA1AAAABAD#####AAp0ZXN0UGhpTnVsACcxLygocGhpPTApKyhhYnMocGhpLXBsYXQpPDAuMDAwMDAwMDAxKSkAAAAJAwAAAAE#8AAAAAAAAAAAAAkAAAAACQgAAAAKAAAANQAAAAEAAAAAAAAAAAAAAAkEAAAAFwAAAAAJAQAAAAoAAAA1AAAACgAAADkAAAABPhEuC+gm1pUAAAAIAP####8AAAAZAAAACgAAAEkAAAAGAP####8BAAAAARAAAAEAAQAAACIAP#AAAAAAAAAAAAAHAP####8BAAAAAQsAAko0AQUAAcBLgAAAAAAAAAAASwAAABIA#####wFmZmYAAQAAACIAAABMAAAAFQD#####AQAAAAAQAAABBQABP#CX6bp5AmEAAABNAAAABgD#####AQAAAAAQAAABAAEAAABOAEAD6BRQ79yc#####wAAAAEAEENJbnREcm9pdGVEcm9pdGUA#####wEAAAAAEAAAAQUAAAAAIwAAAE8AAAATAP####8AAAAjAAAATQAAABQA#####wEAAAAADQACSTQBBQABAAAAUf####8AAAACAAdDUmVwZXJlAP####8AAAAAAQEAAAAiAAAAUgAAAEwAAAAAAAABAAAAAAAAAAAAAAABAAAAAAAAAAAAAAABP#AAAAAAAAAAAAABP#AAAAAAAAAAAAALAP####8BAAAAABAAAAEFAAAAAEwAAABDAAAACAD#####AAAAUAAAABcEAAAACgAAADUAAAALAP####8BAAAAABAAAAEFAAAAAE4AAABV#####wAAAAIADUNMaWV1RGVQb2ludHMA#####wEAf38BAQAAAFYAAABkAAAAAABOAAAABQAAAE4AAABPAAAAUAAAAFUAAABW#####wAAAAEACENWZWN0ZXVyAP####8BAAD#ABAAAAEAAQAAACIAAABUAP####8AAAABABBDUG9pbnREYW5zUmVwZXJlAP####8BAAAAABAAAAEFAAAAAFMAAAAKAAAALgAAAAoAAAA2AAAAIQD#####AQAAAAAQAAABBQAAAABTAAAACgAAAC8AAAAKAAAANwAAACAA#####wH#AAAAEAAAAQABAAAAIgAAAFkAAAAAIAD#####AQB#AAAQAAABAAEAAAAiAAAAWgAAAAAfAP####8BZmZmAQEAAABZAAAAZAAAAAAAKwAAAAYAAAArAAAALAAAAC0AAAAuAAAANgAAAFn#####AAAAAQAMQ1N1cmZhY2VMaWV1AP####8Bf39#AAAABQAAAF0AAAAiAP####8Bf39#AAAABQAAAFcAAAASAP####8B#wAAAQEAAAAZAAAAG#####8AAAABAA1DRGVtaURyb2l0ZU9BAP####8B#wAAAA0AAAEBAQAAABAAAAAT#####wAAAAEADkNQb2ludExpZVBvaW50AP####8B#wAAABAAAVUAQCAAAAAAAADAKgAAAAAAAAUAAAAAFAAAAA0A#####wABdQAAABAAAAATAAAAYv####8AAAABABFDUG9pbnRQYXJBYnNjaXNzZQD#####Af8AAAAQAAJJMgAAAAAAAAAAAEAIAAAAAAAABQAAAAAZAAAAGwAAAAoAAABjAAAAJAD#####AQAAAAALAAJJMQDAEAAAAAAAAEAQAAAAAAAABQAAAABk#####wAAAAEACUNEcm9pdGVBQgD#####AQAAAAANAAABAAEAAAAZAAAAZf####8AAAABABZDRHJvaXRlUGVycGVuZGljdWxhaXJlAP####8BAAAAABAAAAEAAQAAABkAAABmAAAAEgD#####AQAAAAABAAAAGQAAAGUAAAATAP####8AAABnAAAAaAAAABQA#####wEAAAAACwACSjEAwCgAAAAAAADAEAAAAAAAAAUAAgAAAGkAAAAeAP####8AgICAAQEAAAAZAAAAZQAAAGoAAAAAAAABAAAAAAAAAAAAAAABAAAAAAAAAAAAAAABP#AAAAAAAAAAAAABP#AAAAAAAAAAAAAhAP####8BAAAAAA8AAUkAP#AAAAAAAABAEAAAAAAAAAUAAAAAawAAAAoAAAAuAAAACgAAADYAAAAhAP####8BAAAAAA8AAUoBBQAAAABrAAAACgAAAC8AAAAKAAAANwAAACMA#####wEAAAAADQAAAQEBAAAAGQAAAGwAAAAhAP####8BAAAAAA8AAUsAQBAAAAAAAADALgAAAAAAAAUAAAAAawAAAAEAAAAAAAAAAAAAABcEAAAACgAAADUAAAAjAP####8BAAAAAA0AAAEBAQAAABkAAABvAAAAIwD#####AQAAAAANAAABAQEAAAAZAAAAbQAAACAA#####wH#AAAAEAAAAQABAAAAGQAAAGwAAAAAIAD#####AQB#AAAQAAABAAEAAAAZAAAAbQAAAAAgAP####8BAAD#ABAAAAEAAQAAABkAAABvAP####8AAAABAA9DU3ltZXRyaWVBeGlhbGUA#####wAAAHD#####AAAAAQARQ01hY3JvRGlzcGFyaXRpb24A#####wEAAP8B#####w1AfcAAAAAAAECCQAAAAAAAAgHMzP8AAAAAAAAAAAAAAAEAAAAAAAAAAAATKE8sSSxKLEspIGludmlzaWJsZQAAAAAACQAAAHEAAABuAAAAcAAAAHIAAABzAAAAdAAAAG0AAABsAAAAb#####8AAAABABBDTWFjcm9BcHBhcml0aW9uAP####8BAAD#Af####8NQH5wAAAAAABAgxgAAAAAAAIBzMz#AAAAAAAAAAAAAAABAAAAAAAAAAAAEShPLEksSixLKSB2aXNpYmxlAAAAAAAJAAAAcQAAAG4AAABwAAAAcgAAAHMAAAB0AAAAbQAAAGwAAABvAAAAAB4A#####wCAgIABAQAAABkAAABsAAAAbQAAAAAAAAEAAAAAAAAAAAAAAAEAAAAAAAAAAAAAAAE#8AAAAAAAAAAAAAE#8AAAAAAAAAAAACEA#####wHY2NgAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAAGsAAAAKAAAAHgAAAAEAAAAAAAAAAAAAACEA#####wEAAAAAEAABQgAAAAAAAAAAAEAIAAAAAAAABQAAAAB4AAAACgAAAB4AAAABAAAAAAAAAAAAAAAkAP####8BAAAAAA8AAUEBBQAAAAB6AAAADQD#####AARhYnMxAAAAGQAAAGwAAAB7AAAABAD#####AANSYXkABGFiczEAAAAKAAAAfAAAACUA#####wEAAAAAEAAAAQUAAAAAGQAAAGwAAAAJAgAAAAoAAAB9AAAAFwQAAAAKAAAAMQAAACUA#####wEAAAAAEAAAAQUAAAAAGQAAAG0AAAAJAgAAAAoAAAB9AAAAFwMAAAAKAAAAMQAAABEA#####wAAABkAAAB+AAAACwD#####AQAAAAAQAAABBQAAAAB#AAAAgAAAAB8A#####wB#f38BAQAAAIEAAAB4AQAAAAAwAAAABgAAADAAAAAxAAAAfgAAAH8AAACAAAAAgQAAACIA#####wD##wAAAAAFAAAAggAAACEA#####wEAAAAAEAAAAQUAAAAAawAAAAEAAAAAAAAAAAAAAAkBAAAAAQAAAAAAAAAAAAAACgAAAH0AAAASAP####8BAAAAAQEAAAAZAAAAhAAAABMA#####wAAAHEAAACFAAAAFAD#####AQAAAAAQAAABBQABAAAAhgAAAAsA#####wH#AP8AEAAAAQUAAAAAhwAAAEoAAAALAP####8B#wD#ABAAAAEFAAAAAIgAAAAkAAAADAD#####AQAAAAAQAAABAAIAAACIAAAAiQAAAAcA#####wEAAAAAEAAAAQUAAT+0tjyl3q+#AAAAiv####8AAAABAA5DT2JqZXREdXBsaXF1ZQD#####AAAAAAAAAIoAAAANAP####8AAWEAAAAZAAAAbAAAAHsAAAAhAP####8BZmZmABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAAB4AAAACQIAAAAKAAAAjQAAABcEAAAACgAAAAEAAAAJAgAAAAoAAACNAAAAFwMAAAAKAAAAAQAAAB4A#####wDm5uYAAQAAABkAAABsAAAAbwAAAAAAAAEAAAAAAAAAAAAAAAEAAAAAAAAAAAAAAAE#8AAAAAAAAAAAAAE#8AAAAAAAAAAAACEA#####wEAAAAAEAACUyIAwDkAAAAAAADALgAAAAAAAAUAAAAAjwAAAAEAAAAAAAAAAAAAAAoAAAAcAAAAJAD#####AQAAAAAPAAFTAMBEgAAAAAAAwCIAAAAAAAAFAAAAAJAAAAANAP####8ABWFiczExAAAAGQAAAGoAAACRAAAABAD#####AAFzAAVhYnMxMQAAAAoAAACSAAAAKwD#####AAAAAAAAAJH#####AAAAAQAOQ1Rlc3RFeGlzdGVuY2UA#####wAIRXhpc3REZXMAAACSAAAABAD#####AAp0ZXN0U0VnYWxPAA4xLygxLUV4aXN0RGVzKQAAAAkDAAAAAT#wAAAAAAAAAAAACQEAAAABP#AAAAAAAAAAAAAKAAAAlQAAAAgA#####wAAABkAAAAKAAAAlgAAAAQA#####wADeScwAAtrXjIqUmF5XjIvcwAAAAkDAAAACQL#####AAAAAQAKQ1B1aXNzYW5jZQAAAAoAAABIAAAAAUAAAAAAAAAAAAAALQAAAAoAAAB9AAAAAUAAAAAAAAAAAAAACgAAAJMAAAAEAP####8AA3gnMAAUcmFjKFJheV4yLXknMF4yL2teMikAAAAXEgAAAAkBAAAALQAAAAoAAAB9AAAAAUAAAAAAAAAAAAAACQMAAAAtAAAACgAAAJgAAAABQAAAAAAAAAAAAAAtAAAACgAAAEgAAAABQAAAAAAAAAAAAAAhAP####8B#wAAABAAAAEFAAAAAGsAAAAKAAAAmQAAAAoAAACYAAAACwD#####Af8AAAAQAAABBQAAAACaAAAAdQAAAAYA#####wEAAAAAEAAAAQEBAAAAmgA#8zMzMzMzMwAAAAYA#####wEAAAAAEAAAAQEBAAAAmwA#8zMzMzMzMwAAABMA#####wAAAJ0AAACFAAAAFAD#####AQAAAAAQAAABBQACAAAAngAAABMA#####wAAAJwAAACFAAAAFAD#####AQAAAAAQAAABBQACAAAAoAAAABgA#####wEAAAABAQAAABkAAACfAAAAoQAAABUA#####wEAAAAACwACVzMAwCQAAAAAAABAGAAAAAAAAAUAAT#T+ibKoaWlAAAAov####8AAAABAA1DUG9pbnRQcm9qZXRlAP####8BAAAAAAsAAlcyAMAuAAAAAAAAQBQAAAAAAAAFAAAAAKMAAABmAAAAJQD#####AQAAAAALAAJXNQDAIAAAAAAAAEAgAAAAAAAABQAAAACkAAAAo#####8AAAABAA1DRm9uY3Rpb24zVmFyAAAAAAkCAAAACQcAAAAKAAAANQAAAAEAAAAAAAAAAAAAAAkGAAAACgAAADUAAAAKAAAAOgAAAAoAAABIAAAACQEAAAABAAAAAAAAAAAAAAAKAAAASAAAAAQA#####wAIdGVzdFNpbnQAFjEvKGFicyhzKTw9YWJzKGspKlJheSkAAAAJAwAAAAE#8AAAAAAAAAAAAAkGAAAAFwAAAAAKAAAAkwAAAAkCAAAAFwAAAAAKAAAASAAAAAoAAAB9AAAADAD#####AAAAAAAQAAABAAIAAACRAAAAmgAAAAwA#####wAAAAAAEAAAAQACAAAAkQAAAJsAAAAMAP####8Bf39#ABAAAAEAAQAAAJEAAAClAAAABwD#####AQAAAAALAAJXNgEFAAE#6TBqC7jF5AAAAKkAAAAfAP####8Bf39#AAEAAACqAAAAUAAAAAAAowAAAAUAAACjAAAApAAAAKUAAACpAAAAqv####8AAAACABJDTGlldU9iamV0UGFyUHRMaWUA#####wDY2NgAAACrAAAAAUAkAAAAAAAAAAAAqgAAAAIAAACqAAAAqwAAAB8A#####wEAAAAAAgAAAKUAAAB4AAAAAACjAAAAAwAAAKMAAACkAAAApQAAAAgA#####wAAABkAAAAKAAAApgAAAAsA#####wH#AP8AEAAAAQUAAAAAkQAAAK4AAAAMAP####8Bf39#ABAAAAEAAQAAAK8AAACBAAAAMAD#####AH9#fwAAALAAAAABQDUAAAAAAAAAAAAwAAAABwAAADAAAAAxAAAAfgAAAH8AAACAAAAAgQAAALAAAAAHAP####8Bf39#ABAAAAEFAAE#6MY8Xi4nRgAAALAAAAAfAP####8Bf39#AAEAAACyAAAAUAEAAAAAMAAAAAgAAAAwAAAAMQAAAH4AAAB#AAAAgAAAAIEAAACwAAAAsgAAADAA#####wB#f38AAACzAAAAAUAkAAAAAAAAAAAAsgAAAAIAAACyAAAAswAAACsA#####wAAAAAAAACtAAAACAD#####AAAAkQAAAAoAAACmAAAACwD#####Af8AAAAQAAABBQAAAACBAAAAtgAAAB8A#####wEAAAAAAgAAALcAAABkAQAAAAAwAAAABwAAADAAAAAxAAAAfgAAAH8AAACAAAAAgQAAALcAAAArAP####8AAAAAAAAAuAAAAAsA#####wH#AAAAEAAAAQUAAAAAhAAAAJcAAAASAP####8BAAAAAAIAAAAZAAAAugAAABUA#####wEAAAAAEAAAAQUAAUACcpnT3JQVAAAAuwAAAAwA#####wF#f38AEAAAAQABAAAAGQAAALwAAAAHAP####8Bf39#ABAAAAEFAAE#6c331KusFwAAAL0AAAASAP####8Bf39#AAEAAAAZAAAAvgAAADAA#####wB#f38AAAC9AAAAAUA0AAAAAAAAAAAAvAAAAAIAAAC8AAAAvQAAADAA#####wB#f38AAAC#AAAAAUAkAAAAAAAAAAAAvgAAAAIAAAC+AAAAvwAAACsA#####wAAAAAAAAC7AAAADAD#####AQAAAAAQAAABAAIAAACJAAAAkQAAAAcA#####wF#f38AEAAAAQUAAT#B0fQhYRklAAAAwwAAAAYA#####wF#f38AEAAAAQABAAAAxAE#8zMzMzMzMwAAAAwA#####wEAAAAAEAAAAQACAAAAkQAAAIgAAAAdAP####8Bf39#ABAAAAEFAAAAAMUAAADGAAAADAD#####AX9#fwAQAAABAAEAAADEAAAAxwAAADAA#####wB#f38AAADIAAAAAUAkAAAAAAAAAAAAxAAAAAQAAADEAAAAxQAAAMcAAADIAAAADAD#####AX9#fwAQAAABAAEAAACRAAAAiwAAADAA#####wB#f38AAADKAAAAAUAkAAAAAAAAAAAAiwAAAAIAAACLAAAAygAAACsA#####wAAAAAAAADDAAAAKwD#####AAAAAAAAAMYAAAAMAP####8BAAAAABAAAAEBAQAAAJEAAACO#####wAAAAIAFUNMaWV1T2JqZXRQYXJWYXJpYWJsZQD#####AL29vQAAAM4AAAABQDkAAAAAAAAAAAABAAAAAwAAAAEAAACOAAAAzgAAACEA#####wAAAAAAEAACTycAwDkAAAAAAADAKgAAAAAAAAUAAAAAjwAAAAEAAAAAAAAAAAAAAAkBAAAACgAAABwAAAAKAAAAHf####8AAAABABBDRHJvaXRlUGFyYWxsZWxlAP####8B5ubmABAAAAEAAQAAANAAAABuAAAADAD#####AObm5gAQAAABAAEAAACRAAAAfgAAAB0A#####wGkpKQAEAACUCIAAAAAAAAAAABACAAAAAAAAAUAAAAA0QAAANIAAAAyAP####8B5ubmABAAAAEAAQAAANAAAABxAAAADAD#####AObm5gAQAAABAAEAAAB#AAAAkQAAAB0A#####wGkpKQAEAACUSIAwDsAAAAAAADAIgAAAAAAAAUAAAAA1AAAANUAAAARAP####8AAADQAAAA0wAAAAsA#####wGkpKQAEAACUCcAAAAAAAAAAABACAAAAAAAAAUAAAAA1gAAANcAAAAfAP####8ApKSkAQEAAADYAAAAeAEAAAAAKwAAAB4AAAArAAAALAAAAC0AAAAuAAAALwAAADYAAAA3AAAAbAAAAG0AAABuAAAAcQAAAHgAAAB6AAAAewAAAHwAAAB9AAAAfgAAAH8AAACPAAAAkAAAAJEAAADQAAAA0QAAANIAAADTAAAA1AAAANUAAADWAAAA1wAAANgAAAAiAP####8A#wAAAAAABQAAANkAAAATAP####8AAABnAAAAYAAAABQA#####wH#AAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAEAAADbAAAAFAD#####Af8AAAAQAAJKIgAAAAAAAAAAAEAIAAAAAAAABQACAAAA2wAAAB4A#####wDm5uYAAQAAABkAAAAbAAAA3QAAAAAAAAEAAAAAAAAAAAAAAAEAAAAAAAAAAAAAAAE#8AAAAAAAAAAAAAE#8AAAAAAAAP####8AAAACAAxDQ29tbWVudGFpcmUA#####wH#AAAB#####xBAf7gAAAAAAEB7KFHrhR64AgAAAAAAAAAAAAAAAAEAAAAAAAAAAAAEWk9PTQAAAAgA#####wAAABkAAAABP#B64UeuFHsAAAALAP####8B#wAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAACRAAAA4AAAADMA#####wAAAAAAwDQAAAAAAADAKAAAAAAAAAAAAOEQAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAABUwAAABMA#####wAAABoAAACFAAAAFAD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAgAAAOMAAAAUAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQABAAAA4wAAAAwA#####wAAAAAAEAAAAQEBAAAAkAAAAOUAAAAGAP####8BAAAAARAAAAEBAQAAANABP#AAAAAAAAAAAAAdAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAADnAAAA5gAAAAwA#####wB#f38AEAAAAQEBAAAA0AAAAOgAAAAMAP####8AAAAAABAAAAEBAQAAABkAAADlAAAADAD#####AAAAAAAQAAABAQEAAAAZAAAAkf####8AAAACAAlDQ2VyY2xlT1IA#####wEAAAABAQAAANAAAAABP9mZmZmZmZoAAAAAEwD#####AAAA6QAAAOwAAAAUAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQABAAAA7QAAABQA#####wAAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAIAAADtAAAAEwD#####AAAA6wAAAOwAAAAUAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQACAAAA8AAAABQA#####wEAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAEAAADwAAAACAD#####AAAA0AAAABcEAAAACgAAADUAAAALAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAADyAAAA8wAAABEA#####wAAANAAAAD0AAAACwD#####AQAAAAAQAAAAQAgAAAAAAAAAAAAAAAAAAAUAAAAA7gAAAPUAAAAMAP####8AAAAAABAAAAEBAQAAAPQAAADQAAAADAD#####AAAAAAAQAAABAQEAAADQAAAA7gAAAAwA#####wAAAAAAEAAAAQEBAAAA7gAAAPYAAAAMAP####8AAAAAABAAAAEBAQAAAPYAAAD0#####wAAAAEACUNQb2x5Z29uZQD#####AAAAAAEBAAAABQAAAPQAAADQAAAA7gAAAPYAAAD0AAAAEQD#####AAAA0AAAAO4AAAALAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAAAZAAAA#AAAAAsA#####wEAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAABkAAAD1AAAAEQD#####AAAAGQAAAP4AAAALAP####8BAAAAABAAAABACAAAAAAAAAAAAAAAAAAABQAAAAD9AAAA#wAAAAwA#####wAAAAAAEAAAAQEBAAAA#gAAABkAAAAMAP####8AAAAAABAAAAEBAQAAABkAAAD9AAAADAD#####AAAAAAAQAAABAQEAAAD9AAABAAAAAAwA#####wAAAAAAEAAAAQEBAAABAAAAAP4AAAA1AP####8AAAAAAQEAAAAFAAAA#gAAABkAAAD9AAABAAAAAP4AAAAGAP####8BAAAAARAAAAEBAQAAABABP#AAAAAAAAAAAAA0AP####8BAAAAAQEAAAAQAAAAAT#JmZmZmZmaAAAAABMA#####wAAAQYAAAEHAAAAFAD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAQAAAQgAAAAUAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQACAAABCAAAAAwA#####wH#AAAAEAAAAQABAAABCgAAAQn#####AAAAAQAHQ01pbGlldQD#####Af8AAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAA0AAAAJAAAAA2AP####8B#wAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAAAZAAAA0AAAAA4A#####wEAAAAAwCoAAAAAAADAHAAAAAAAAAAAAQwQAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAAAAAACAAAAHQAAADYA#####wEAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAAHkAAAAZAAAADgD#####AQAAAADAHAAAAAAAAAAAAAAAAAAAAAABDxAAAAAAAAAAAAAAAAAAAQAAAAAAAAAAAAAAAAIAAAAeAAAABAD#####AAJoMwAFaDEtaDIAAAAJAQAAAAoAAAAcAAAACgAAAB0AAAAOAP####8BAAAAAMA1AAAAAAAAwCIAAAAAAAAAAAENEAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAQAAAREAAAAY##########8='
        if (!context.isHtml) { texte = '\\begin{minipage}{0.7 \\linewidth} \n\t' } else { texte = '' }
        texte += `Un cône a pour rayon $${texNombre(r, 1)}$${sp()}cm et pour hauteur $SO${sp()}=${sp()}${texNombre(h1, 1)}${sp()}$cm.<br>Le point O' est situé sur la hauteur [SO] à ${texNombre(h2, 0)}${sp()}cm de S.<br>`
        texte += 'Un plan parallèle à la base passant par O\' coupe le cône.<br>'
        texte += 'On obtient ainsi une section ' + katexPopup2(numeroExercice, 1, 'semblable', 'Définition : Figures semblables', 'Se dit de deux figures/solides qui ont les mêmes formes, les mêmes angles mais pas nécessairement les mêmes mesures.<br>Les représentations d\'une même figure à deux échelles différentes sont des figures semblables.') + ' à la base et un cône réduit semblable au grand cône.<br>'
        if (!context.isHtml) { texte += 'La figure n\'est pas en vraie grandeur.<br>' }
        texte += numAlpha(0) + ' Calculer l\'' + katexPopup2(numeroExercice + 1, 1, 'aire de base du cône', 'Formule : Aire du disque de rayon R', '$Aire=\\pi \\times \\text{R}^{2}$') + '.<br>'
        texte += numAlpha(1) + ' Calculer le ' + katexPopup2(numeroExercice + 6, 1, 'volume du cône', 'Formule : Volume d\'un cône de rayon R et de hauteur h', '$Volume= \\dfrac{\\pi \\times \\text{R}^{2} \\times \\text{h}}{3}$') + '.<br>'
        texte += numAlpha(2) + ' En déduire l\'aire de la ' + katexPopup2(numeroExercice + 11, 1, 'section', 'Définition : Section plane d\'un solide', `La section d'un solide par un plan est une figure plane.<br>Dans le cas d'une section d'un cône par un plan parallèle à sa base, cette section est un disque qui est une réduction de la base.<br>Dans une réduction de coefficient k, les aires sont multipliées par k${texteExposant(2)} et les volumes sont multipliés par k${texteExposant(3)}.`) + ` sachant que SO'${sp()}=${sp()}${texNombre(h2, 0)}${sp()}cm.<br>`
        texte += numAlpha(3) + ' Calculer le volume du cône de hauteur SO\'.<br>'
        texte += numAlpha(4) + ' Calculer le volume du tronc de cône (partie du cône située entre la base et la section).'
        if (context.isHtml) { texte += '<br>Le point O peut être déplacé et on peut changer l\'angle de vue &#x3C6; ' } else {
          texte += `\n\t \\end{minipage} \n\t \\begin{minipage}{0.3 \\linewidth} \n\t \\begin{tikzpicture}[scale=0.7] \n\t 
          \\definecolor{hhhhhh}{rgb}{0,0,0}
          \\definecolor{phphph}{rgb}{0.5,0.5,0.5}
          \\definecolor{ofofof}{rgb}{0.5,0.5,0.5}
          \\definecolor{ffffhh}{rgb}{1,1,0}
          \\definecolor{enenen}{rgb}{0.9,0.9,0.9}
          \\definecolor{dpdpdp}{rgb}{0.85,0.85,0.85}
          \\definecolor{bdbdbd}{rgb}{0.74,0.74,0.74}
          \\definecolor{alalal}{rgb}{0.64,0.64,0.64}
          \\definecolor{ffhhhh}{rgb}{1,0,0}
          \\clip (40.89,0) rectangle (0,22.58);
          \\fill[color=black] (4.609,10.281) circle (0.063);
          \\node at (3.828, 10.531) [align=left,inner sep = 0pt, outer sep = 0pt,below right,black,font= \\sf \\fontsize {0.438cm} {0.547cm} \\selectfont] {$\\text{O}$};
          \\draw [color=ofofof , dotted, line width = 0.4](1.513,9.062)--(1.679,9)--(1.853,8.942)--(2.035,8.887)--(2.224,8.836)--(2.419,8.788)--(2.621,8.745)--(2.827,8.706)--(3.039,8.672)--(3.255,8.642)--(3.475,8.616)--(3.698,8.595)--(3.923,8.578)--(4.15,8.567)--(4.379,8.559)--(4.608,8.557)--(4.837,8.559)--(5.065,8.566)--(5.292,8.578)--(5.518,8.595)--(5.741,8.616)--(5.96,8.641)--(6.176,8.671)--(6.388,8.706)--(6.595,8.745)--(6.796,8.788)--(6.992,8.835)--(7.181,8.886)--(7.363,8.941)--(7.537,8.999)--(7.703,9.062)--(7.861,9.127)--(8.01,9.196)--(8.15,9.267)--(8.279,9.342)--(8.399,9.419)--(8.509,9.498)--(8.607,9.579)--(8.695,9.663)--(8.772,9.748)--(8.837,9.834)--(8.891,9.922)--(8.932,10.011)--(8.962,10.1)--(8.98,10.19)--(8.987,10.281)--(8.981,10.371)--(8.963,10.461)--(8.933,10.55)--(8.891,10.639)--(8.838,10.727)--(8.773,10.813)--(8.696,10.899)--(8.609,10.982)--(8.51,11.063)--(8.401,11.143)--(8.281,11.22)--(8.152,11.294)--(8.012,11.366)--(7.863,11.435)--(7.706,11.5)--(7.54,11.562)--(7.365,11.621)--(7.184,11.676)--(6.995,11.727)--(6.799,11.774)--(6.598,11.817)--(6.391,11.856)--(6.18,11.891)--(5.964,11.921)--(5.744,11.947)--(5.521,11.968)--(5.296,11.984)--(5.069,11.996)--(4.84,12.003)--(4.611,12.006)--(4.382,12.003)--(4.154,11.996)--(3.926,11.984)--(3.701,11.968)--(3.478,11.947)--(3.258,11.921)--(3.042,11.891)--(2.831,11.857)--(2.624,11.818)--(2.422,11.775)--(2.227,11.728)--(2.038,11.677)--(1.856,11.622)--(1.682,11.563)--(1.515,11.501)--(1.358,11.436)--(1.209,11.367)--(1.069,11.295)--(0.939,11.221)--(0.819,11.144)--(0.71,11.065)--(0.611,10.983)--(0.524,10.9)--(0.447,10.815)--(0.382,10.728)--(0.328,10.64)--(0.286,10.552)--(0.256,10.462)--(0.238,10.372)--(0.232,10.282)--(0.238,10.192)--(0.256,10.102)--(0.286,10.012)--(0.327,9.923)--(0.381,9.836)--(0.446,9.749)--(0.522,9.664)--(0.61,9.581)--(0.708,9.499)--(0.818,9.42)--(0.937,9.343)--(1.067,9.268)--(1.207,9.197)--(1.355,9.128)--cycle;
          
          \\fill[color = ffffhh, opacity = 0.2](1.513,9.062)--(1.679,9)--(1.853,8.942)--(2.035,8.887)--(2.224,8.836)--(2.419,8.788)--(2.621,8.745)--(2.827,8.706)--(3.039,8.672)--(3.255,8.642)--(3.475,8.616)--(3.698,8.595)--(3.923,8.578)--(4.15,8.567)--(4.379,8.559)--(4.608,8.557)--(4.837,8.559)--(5.065,8.566)--(5.292,8.578)--(5.518,8.595)--(5.741,8.616)--(5.96,8.641)--(6.176,8.671)--(6.388,8.706)--(6.595,8.745)--(6.796,8.788)--(6.992,8.835)--(7.181,8.886)--(7.363,8.941)--(7.537,8.999)--(7.703,9.062)--(7.861,9.127)--(8.01,9.196)--(8.15,9.267)--(8.279,9.342)--(8.399,9.419)--(8.509,9.498)--(8.607,9.579)--(8.695,9.663)--(8.772,9.748)--(8.837,9.834)--(8.891,9.922)--(8.932,10.011)--(8.962,10.1)--(8.98,10.19)--(8.987,10.281)--(8.981,10.371)--(8.963,10.461)--(8.933,10.55)--(8.891,10.639)--(8.838,10.727)--(8.773,10.813)--(8.696,10.899)--(8.609,10.982)--(8.51,11.063)--(8.401,11.143)--(8.281,11.22)--(8.152,11.294)--(8.012,11.366)--(7.863,11.435)--(7.706,11.5)--(7.54,11.562)--(7.365,11.621)--(7.184,11.676)--(6.995,11.727)--(6.799,11.774)--(6.598,11.817)--(6.391,11.856)--(6.18,11.891)--(5.964,11.921)--(5.744,11.947)--(5.521,11.968)--(5.296,11.984)--(5.069,11.996)--(4.84,12.003)--(4.611,12.006)--(4.382,12.003)--(4.154,11.996)--(3.926,11.984)--(3.701,11.968)--(3.478,11.947)--(3.258,11.921)--(3.042,11.891)--(2.831,11.857)--(2.624,11.818)--(2.422,11.775)--(2.227,11.728)--(2.038,11.677)--(1.856,11.622)--(1.682,11.563)--(1.515,11.501)--(1.358,11.436)--(1.209,11.367)--(1.069,11.295)--(0.939,11.221)--(0.819,11.144)--(0.71,11.065)--(0.611,10.983)--(0.524,10.9)--(0.447,10.815)--(0.382,10.728)--(0.328,10.64)--(0.286,10.552)--(0.256,10.462)--(0.238,10.372)--(0.232,10.282)--(0.238,10.192)--(0.256,10.102)--(0.286,10.012)--(0.327,9.923)--(0.381,9.836)--(0.446,9.749)--(0.522,9.664)--(0.61,9.581)--(0.708,9.499)--(0.818,9.42)--(0.937,9.343)--(1.067,9.268)--(1.207,9.197)--(1.355,9.128)(1.513,9.062);
          \\draw [color=black , line width = 0.8](4.609,21.776)--(8.937,10.54);
          \\draw [color=black , line width = 0.8](4.609,21.776)--(0.282,10.54);
          \\draw [color=dpdpdp , line width = 0.4](4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776)--(4.609,21.776);
          
          \\draw [color=dpdpdp , line width = 0.4](4.129,20.528)--(4.126,20.52)--(4.124,20.511)--(4.123,20.503)--(4.123,20.495)--(4.124,20.486)--(4.126,20.478)--(4.129,20.47)--(4.133,20.461)--(4.137,20.453)--(4.143,20.445)--(4.149,20.437)--(4.156,20.429)--(4.164,20.422)--(4.173,20.414)--(4.183,20.407)--(4.194,20.399)--(4.205,20.392)--(4.217,20.386)--(4.23,20.379)--(4.244,20.373)--(4.258,20.366)--(4.273,20.361)--(4.289,20.355)--(4.305,20.35)--(4.322,20.344)--(4.339,20.34)--(4.357,20.335)--(4.376,20.331)--(4.395,20.327)--(4.414,20.324)--(4.433,20.32)--(4.453,20.318)--(4.473,20.315)--(4.494,20.313)--(4.515,20.311)--(4.535,20.31)--(4.556,20.309)--(4.578,20.308)--(4.599,20.308)--(4.62,20.308)--(4.641,20.308)--(4.662,20.309)--(4.683,20.31)--(4.704,20.311)--(4.725,20.313)--(4.745,20.315)--(4.766,20.318)--(4.785,20.32)--(4.805,20.324)--(4.824,20.327)--(4.843,20.331)--(4.861,20.335)--(4.879,20.34)--(4.897,20.344)--(4.913,20.35)--(4.93,20.355)--(4.945,20.361)--(4.96,20.366)--(4.975,20.373)--(4.988,20.379)--(5.001,20.386)--(5.013,20.392)--(5.025,20.399)--(5.035,20.407)--(5.045,20.414)--(5.054,20.422)--(5.062,20.429)--(5.07,20.437)--(5.076,20.445)--(5.082,20.453)--(5.086,20.461)--(5.09,20.47)--(5.093,20.478)--(5.095,20.486)--(5.096,20.495)--(5.096,20.503)--(5.095,20.511)--(5.093,20.52)--(5.09,20.528);
          
          \\draw [color=dpdpdp , line width = 0.4](3.648,19.279)--(3.642,19.263)--(3.639,19.246)--(3.637,19.229)--(3.637,19.213)--(3.639,19.196)--(3.643,19.179)--(3.648,19.163)--(3.656,19.146)--(3.665,19.13)--(3.676,19.114)--(3.689,19.098)--(3.703,19.082)--(3.72,19.067)--(3.738,19.052)--(3.757,19.037)--(3.778,19.023)--(3.801,19.009)--(3.826,18.995)--(3.851,18.982)--(3.879,18.969)--(3.907,18.957)--(3.937,18.945)--(3.969,18.934)--(4.001,18.923)--(4.035,18.913)--(4.07,18.903)--(4.105,18.894)--(4.142,18.886)--(4.18,18.878)--(4.218,18.871)--(4.257,18.865)--(4.297,18.859)--(4.338,18.854)--(4.378,18.85)--(4.42,18.846)--(4.462,18.843)--(4.504,18.841)--(4.546,18.84)--(4.588,18.839)--(4.631,18.839)--(4.673,18.84)--(4.715,18.841)--(4.757,18.843)--(4.799,18.846)--(4.84,18.85)--(4.881,18.854)--(4.922,18.859)--(4.962,18.865)--(5.001,18.871)--(5.039,18.878)--(5.077,18.886)--(5.113,18.894)--(5.149,18.903)--(5.184,18.913)--(5.218,18.923)--(5.25,18.934)--(5.281,18.945)--(5.311,18.957)--(5.34,18.969)--(5.367,18.982)--(5.393,18.995)--(5.417,19.009)--(5.44,19.023)--(5.462,19.037)--(5.481,19.052)--(5.499,19.067)--(5.515,19.082)--(5.53,19.098)--(5.543,19.114)--(5.554,19.13)--(5.563,19.146)--(5.57,19.163)--(5.576,19.179)--(5.58,19.196)--(5.582,19.213)--(5.582,19.229)--(5.58,19.246)--(5.577,19.263)--(5.571,19.279);
          
          \\draw [color=dpdpdp , line width = 0.4](3.167,18.031)--(3.159,18.006)--(3.153,17.981)--(3.151,17.956)--(3.151,17.931)--(3.154,17.906)--(3.159,17.881)--(3.168,17.856)--(3.179,17.832)--(3.193,17.807)--(3.209,17.783)--(3.228,17.759)--(3.25,17.736)--(3.275,17.712)--(3.302,17.69)--(3.331,17.668)--(3.363,17.646)--(3.397,17.625)--(3.434,17.604)--(3.472,17.584)--(3.513,17.565)--(3.556,17.547)--(3.601,17.529)--(3.648,17.512)--(3.697,17.496)--(3.748,17.481)--(3.8,17.466)--(3.853,17.453)--(3.908,17.441)--(3.965,17.429)--(4.022,17.418)--(4.081,17.409)--(4.141,17.4)--(4.202,17.393)--(4.263,17.386)--(4.325,17.381)--(4.388,17.377)--(4.451,17.373)--(4.514,17.371)--(4.578,17.37)--(4.641,17.37)--(4.705,17.371)--(4.768,17.373)--(4.831,17.377)--(4.894,17.381)--(4.956,17.386)--(5.017,17.393)--(5.078,17.4)--(5.138,17.409)--(5.196,17.418)--(5.254,17.429)--(5.31,17.441)--(5.365,17.453)--(5.419,17.466)--(5.471,17.481)--(5.522,17.496)--(5.57,17.512)--(5.617,17.529)--(5.662,17.547)--(5.705,17.565)--(5.746,17.584)--(5.785,17.604)--(5.822,17.625)--(5.856,17.646)--(5.888,17.668)--(5.917,17.69)--(5.944,17.712)--(5.968,17.736)--(5.99,17.759)--(6.009,17.783)--(6.026,17.807)--(6.04,17.832)--(6.051,17.856)--(6.059,17.881)--(6.065,17.906)--(6.068,17.931)--(6.068,17.956)--(6.066,17.981)--(6.06,18.006)--(6.052,18.031);
          
          \\draw [color=dpdpdp , line width = 0.4](2.686,16.782)--(2.675,16.749)--(2.668,16.716)--(2.664,16.683)--(2.665,16.649)--(2.668,16.616)--(2.676,16.583)--(2.687,16.549)--(2.702,16.517)--(2.72,16.484)--(2.743,16.452)--(2.768,16.42)--(2.797,16.389)--(2.83,16.358)--(2.866,16.327)--(2.905,16.298)--(2.948,16.269)--(2.993,16.241)--(3.042,16.214)--(3.094,16.187)--(3.148,16.162)--(3.205,16.137)--(3.265,16.113)--(3.328,16.091)--(3.393,16.069)--(3.46,16.049)--(3.53,16.03)--(3.601,16.012)--(3.675,15.995)--(3.75,15.98)--(3.827,15.966)--(3.905,15.953)--(3.985,15.942)--(4.066,15.932)--(4.148,15.923)--(4.23,15.916)--(4.314,15.91)--(4.398,15.906)--(4.482,15.903)--(4.567,15.901)--(4.652,15.901)--(4.736,15.903)--(4.821,15.906)--(4.905,15.91)--(4.988,15.916)--(5.071,15.923)--(5.153,15.932)--(5.234,15.942)--(5.314,15.953)--(5.392,15.966)--(5.469,15.98)--(5.544,15.995)--(5.617,16.012)--(5.689,16.03)--(5.758,16.049)--(5.826,16.069)--(5.891,16.091)--(5.953,16.113)--(6.013,16.137)--(6.071,16.162)--(6.125,16.187)--(6.177,16.214)--(6.226,16.241)--(6.271,16.269)--(6.314,16.298)--(6.353,16.327)--(6.389,16.358)--(6.421,16.389)--(6.451,16.42)--(6.476,16.452)--(6.498,16.484)--(6.517,16.517)--(6.532,16.549)--(6.543,16.583)--(6.55,16.616)--(6.554,16.649)--(6.554,16.683)--(6.551,16.716)--(6.544,16.749)--(6.533,16.782);
          
          \\draw [color=dpdpdp , line width = 0.4](2.205,15.534)--(2.192,15.492)--(2.182,15.451)--(2.178,15.409)--(2.178,15.367)--(2.183,15.326)--(2.193,15.284)--(2.207,15.243)--(2.225,15.202)--(2.248,15.161)--(2.276,15.121)--(2.308,15.081)--(2.344,15.042)--(2.385,15.003)--(2.43,14.965)--(2.479,14.928)--(2.532,14.892)--(2.589,14.857)--(2.65,14.823)--(2.715,14.79)--(2.783,14.758)--(2.854,14.727)--(2.929,14.698)--(3.008,14.669)--(3.089,14.643)--(3.173,14.617)--(3.26,14.593)--(3.349,14.571)--(3.441,14.55)--(3.535,14.531)--(3.631,14.513)--(3.729,14.497)--(3.829,14.483)--(3.93,14.47)--(4.032,14.46)--(4.136,14.451)--(4.24,14.443)--(4.345,14.438)--(4.451,14.434)--(4.556,14.432)--(4.662,14.432)--(4.768,14.434)--(4.874,14.438)--(4.979,14.443)--(5.083,14.451)--(5.187,14.46)--(5.289,14.47)--(5.39,14.483)--(5.49,14.497)--(5.588,14.513)--(5.684,14.531)--(5.778,14.55)--(5.869,14.571)--(5.959,14.593)--(6.046,14.617)--(6.13,14.643)--(6.211,14.669)--(6.289,14.698)--(6.364,14.727)--(6.436,14.758)--(6.504,14.79)--(6.569,14.823)--(6.63,14.857)--(6.687,14.892)--(6.74,14.928)--(6.789,14.965)--(6.834,15.003)--(6.874,15.042)--(6.911,15.081)--(6.943,15.121)--(6.97,15.161)--(6.994,15.202)--(7.012,15.243)--(7.026,15.284)--(7.036,15.326)--(7.04,15.367)--(7.041,15.409)--(7.036,15.451)--(7.027,15.492)--(7.014,15.534);
          
          \\draw [color=dpdpdp , line width = 0.4](1.724,14.285)--(1.708,14.236)--(1.697,14.186)--(1.692,14.136)--(1.692,14.086)--(1.698,14.036)--(1.709,13.986)--(1.726,13.936)--(1.748,13.887)--(1.776,13.838)--(1.809,13.79)--(1.848,13.742)--(1.891,13.695)--(1.94,13.648)--(1.994,13.603)--(2.053,13.559)--(2.117,13.515)--(2.185,13.473)--(2.258,13.432)--(2.336,13.392)--(2.417,13.354)--(2.503,13.317)--(2.593,13.282)--(2.687,13.248)--(2.785,13.216)--(2.886,13.185)--(2.99,13.157)--(3.097,13.13)--(3.207,13.105)--(3.32,13.082)--(3.435,13.061)--(3.553,13.041)--(3.673,13.024)--(3.794,13.009)--(3.917,12.996)--(4.041,12.985)--(4.166,12.977)--(4.292,12.97)--(4.419,12.966)--(4.546,12.964)--(4.673,12.964)--(4.8,12.966)--(4.927,12.97)--(5.053,12.977)--(5.178,12.985)--(5.302,12.996)--(5.425,13.009)--(5.546,13.024)--(5.666,13.041)--(5.783,13.061)--(5.899,13.082)--(6.011,13.105)--(6.122,13.13)--(6.229,13.157)--(6.333,13.185)--(6.434,13.216)--(6.531,13.248)--(6.625,13.282)--(6.715,13.317)--(6.801,13.354)--(6.883,13.392)--(6.961,13.432)--(7.034,13.473)--(7.102,13.515)--(7.166,13.559)--(7.225,13.603)--(7.279,13.648)--(7.328,13.695)--(7.371,13.742)--(7.41,13.79)--(7.443,13.838)--(7.47,13.887)--(7.493,13.936)--(7.51,13.986)--(7.521,14.036)--(7.527,14.086)--(7.527,14.136)--(7.522,14.186)--(7.511,14.236)--(7.494,14.285);
          
          \\draw [color=dpdpdp , line width = 0.4](1.243,13.037)--(1.224,12.979)--(1.212,12.921)--(1.206,12.862)--(1.206,12.804)--(1.213,12.745)--(1.226,12.687)--(1.245,12.629)--(1.271,12.572)--(1.304,12.515)--(1.342,12.458)--(1.387,12.403)--(1.438,12.348)--(1.495,12.294)--(1.558,12.241)--(1.627,12.189)--(1.701,12.139)--(1.781,12.089)--(1.866,12.041)--(1.957,11.995)--(2.052,11.95)--(2.152,11.907)--(2.257,11.866)--(2.367,11.827)--(2.481,11.789)--(2.598,11.754)--(2.72,11.72)--(2.845,11.689)--(2.974,11.66)--(3.105,11.633)--(3.24,11.608)--(3.377,11.586)--(3.516,11.566)--(3.658,11.548)--(3.801,11.533)--(3.946,11.52)--(4.092,11.51)--(4.239,11.503)--(4.387,11.497)--(4.535,11.495)--(4.684,11.495)--(4.832,11.497)--(4.98,11.503)--(5.127,11.51)--(5.273,11.52)--(5.418,11.533)--(5.561,11.548)--(5.702,11.566)--(5.842,11.586)--(5.979,11.608)--(6.113,11.633)--(6.245,11.66)--(6.374,11.689)--(6.499,11.72)--(6.62,11.754)--(6.738,11.789)--(6.852,11.827)--(6.961,11.866)--(7.066,11.907)--(7.167,11.95)--(7.262,11.995)--(7.353,12.041)--(7.438,12.089)--(7.518,12.139)--(7.592,12.189)--(7.661,12.241)--(7.724,12.294)--(7.781,12.348)--(7.831,12.403)--(7.876,12.458)--(7.915,12.515)--(7.947,12.572)--(7.973,12.629)--(7.993,12.687)--(8.006,12.745)--(8.013,12.804)--(8.013,12.862)--(8.007,12.921)--(7.994,12.979)--(7.975,13.037);
          
          \\draw [color=dpdpdp , line width = 0.4](0.763,11.788)--(0.741,11.722)--(0.726,11.656)--(0.719,11.589)--(0.72,11.522)--(0.727,11.455)--(0.742,11.389)--(0.765,11.323)--(0.795,11.257)--(0.832,11.192)--(0.876,11.127)--(0.927,11.064)--(0.985,11.001)--(1.05,10.939)--(1.122,10.879)--(1.201,10.819)--(1.286,10.762)--(1.377,10.705)--(1.474,10.651)--(1.578,10.598)--(1.687,10.547)--(1.801,10.498)--(1.921,10.45)--(2.047,10.405)--(2.177,10.362)--(2.311,10.322)--(2.45,10.283)--(2.593,10.248)--(2.74,10.214)--(2.89,10.183)--(3.044,10.155)--(3.201,10.13)--(3.36,10.107)--(3.522,10.087)--(3.686,10.07)--(3.851,10.055)--(4.018,10.044)--(4.186,10.035)--(4.355,10.029)--(4.525,10.026)--(4.694,10.026)--(4.864,10.029)--(5.032,10.035)--(5.201,10.044)--(5.368,10.055)--(5.533,10.07)--(5.697,10.087)--(5.859,10.107)--(6.018,10.13)--(6.175,10.155)--(6.328,10.183)--(6.479,10.214)--(6.626,10.248)--(6.769,10.283)--(6.908,10.322)--(7.042,10.362)--(7.172,10.405)--(7.297,10.45)--(7.417,10.498)--(7.532,10.547)--(7.641,10.598)--(7.744,10.651)--(7.842,10.705)--(7.933,10.762)--(8.018,10.819)--(8.097,10.879)--(8.168,10.939)--(8.234,11.001)--(8.292,11.064)--(8.343,11.127)--(8.387,11.192)--(8.424,11.257)--(8.454,11.323)--(8.476,11.389)--(8.491,11.455)--(8.499,11.522)--(8.499,11.589)--(8.492,11.656)--(8.478,11.722)--(8.456,11.788);
          
          \\draw [color=dpdpdp , line width = 0.4](0.282,10.54)--(0.257,10.465)--(0.241,10.391)--(0.233,10.315)--(0.233,10.24)--(0.242,10.165)--(0.259,10.09)--(0.284,10.016)--(0.318,9.942)--(0.359,9.869)--(0.409,9.796)--(0.467,9.724)--(0.532,9.654)--(0.605,9.585)--(0.686,9.516)--(0.775,9.45)--(0.87,9.385)--(0.973,9.322)--(1.082,9.26)--(1.199,9.2)--(1.321,9.143)--(1.45,9.088)--(1.586,9.035)--(1.726,8.984)--(1.872,8.936)--(2.024,8.89)--(2.18,8.847)--(2.341,8.807)--(2.506,8.769)--(2.676,8.734)--(2.849,8.703)--(3.025,8.674)--(3.204,8.648)--(3.386,8.626)--(3.57,8.606)--(3.756,8.59)--(3.944,8.577)--(4.133,8.567)--(4.323,8.561)--(4.514,8.557)--(4.705,8.557)--(4.895,8.561)--(5.085,8.567)--(5.274,8.577)--(5.462,8.59)--(5.648,8.606)--(5.833,8.626)--(6.015,8.648)--(6.194,8.674)--(6.37,8.703)--(6.543,8.734)--(6.712,8.769)--(6.878,8.807)--(7.039,8.847)--(7.195,8.89)--(7.346,8.936)--(7.493,8.984)--(7.633,9.035)--(7.768,9.088)--(7.897,9.143)--(8.02,9.2)--(8.136,9.26)--(8.246,9.322)--(8.349,9.385)--(8.444,9.45)--(8.532,9.516)--(8.613,9.585)--(8.687,9.654)--(8.752,9.724)--(8.81,9.796)--(8.859,9.869)--(8.901,9.942)--(8.934,10.016)--(8.96,10.09)--(8.977,10.165)--(8.985,10.24)--(8.986,10.315)--(8.978,10.391)--(8.962,10.465)--(8.937,10.54);
          
          \\draw [color=black , line width = 0.8](0.282,10.54)--(0.265,10.49)--(0.251,10.441)--(0.241,10.391)--(0.235,10.341)--(0.232,10.291)--(0.233,10.242)--(0.238,10.192)--(0.246,10.142)--(0.259,10.092)--(0.274,10.043)--(0.294,9.994)--(0.317,9.944)--(0.343,9.896)--(0.373,9.847)--(0.407,9.799)--(0.444,9.751)--(0.485,9.704)--(0.529,9.657)--(0.576,9.611)--(0.627,9.566)--(0.681,9.52)--(0.739,9.476)--(0.8,9.432)--(0.864,9.389)--(0.931,9.347)--(1.001,9.305)--(1.074,9.265)--(1.15,9.225)--(1.229,9.186)--(1.311,9.148)--(1.396,9.111)--(1.483,9.075)--(1.573,9.039)--(1.665,9.005)--(1.76,8.972)--(1.857,8.94)--(1.957,8.91)--(2.059,8.88)--(2.163,8.851)--(2.269,8.824)--(2.377,8.798)--(2.487,8.773)--(2.598,8.75)--(2.712,8.727)--(2.827,8.706)--(2.943,8.687)--(3.061,8.669)--(3.18,8.652)--(3.3,8.636)--(3.421,8.622)--(3.544,8.609)--(3.667,8.597)--(3.791,8.587)--(3.916,8.579)--(4.041,8.572)--(4.167,8.566)--(4.293,8.561)--(4.419,8.559)--(4.546,8.557)--(4.673,8.557)--(4.799,8.559)--(4.926,8.561)--(5.052,8.566)--(5.178,8.572)--(5.303,8.579)--(5.428,8.587)--(5.552,8.597)--(5.675,8.609)--(5.797,8.622)--(5.919,8.636)--(6.039,8.652)--(6.158,8.669)--(6.276,8.687)--(6.392,8.706)--(6.507,8.727)--(6.62,8.75)--(6.732,8.773)--(6.842,8.798)--(6.95,8.824)--(7.056,8.851)--(7.16,8.88)--(7.262,8.91)--(7.361,8.94)--(7.459,8.972)--(7.554,9.005)--(7.646,9.039)--(7.736,9.075)--(7.823,9.111)--(7.908,9.148)--(7.99,9.186)--(8.069,9.225)--(8.145,9.265)--(8.218,9.305)--(8.288,9.347)--(8.355,9.389)--(8.419,9.432)--(8.48,9.476)--(8.537,9.52)--(8.592,9.566)--(8.643,9.611)--(8.69,9.657)--(8.734,9.704)--(8.775,9.751)--(8.812,9.799)--(8.846,9.847)--(8.876,9.896)--(8.902,9.944)--(8.925,9.994)--(8.945,10.043)--(8.96,10.092)--(8.972,10.142)--(8.981,10.192)--(8.985,10.242)--(8.986,10.291)--(8.984,10.341)--(8.978,10.391)--(8.968,10.441)--(8.954,10.49)--(8.937,10.54);
          
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(1.513,9.062);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(2.419,8.788);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(3.475,8.616);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(4.608,8.557);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(5.741,8.616);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(6.796,8.788);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(7.703,9.062);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(8.399,9.419);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(8.837,9.834);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(8.987,10.281);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(8.838,10.727);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(8.401,11.143);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(7.706,11.5);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(6.799,11.774);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(5.744,11.947);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(4.611,12.006);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(3.478,11.947);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(2.422,11.775);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(1.515,11.501);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(0.819,11.144);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(0.382,10.728);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(0.232,10.282);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(0.381,9.836);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(0.818,9.42);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.609,21.776)--(1.513,9.062);
          \\fill[color=black] (4.609,17.178) circle (0.063);
          \\node at (3.609, 17.46) [align=left,inner sep = 0pt, outer sep = 0pt,below right,black,font= \\sf \\fontsize {0.469cm} {0.586cm} \\selectfont] {$\\text{O'}$};
          \\draw [color=enenen , line width = 0.4](4.609,21.776)--(4.213,10.125);
          \\draw [color=enenen , line width = 0.4](1.541,11.491)--(4.609,21.776);
          \\draw [color=alalal , dotted, line width = 0.4](2.887,17.055)--(2.905,17.02)--(2.929,16.985)--(2.956,16.951)--(2.989,16.917)--(3.025,16.885)--(3.066,16.853)--(3.111,16.821)--(3.16,16.791)--(3.213,16.762)--(3.27,16.734)--(3.33,16.707)--(3.394,16.682)--(3.461,16.658)--(3.531,16.635)--(3.604,16.614)--(3.68,16.594)--(3.758,16.576)--(3.839,16.559)--(3.921,16.544)--(4.006,16.531)--(4.092,16.519)--(4.179,16.51)--(4.268,16.502)--(4.358,16.496)--(4.448,16.492)--(4.539,16.489)--(4.629,16.489)--(4.72,16.49)--(4.811,16.493)--(4.901,16.498)--(4.99,16.505)--(5.078,16.514)--(5.165,16.524)--(5.251,16.537)--(5.334,16.55)--(5.416,16.566)--(5.496,16.583)--(5.573,16.602)--(5.647,16.623)--(5.719,16.645)--(5.788,16.668)--(5.854,16.693)--(5.916,16.719)--(5.975,16.746)--(6.03,16.775)--(6.081,16.805)--(6.128,16.835)--(6.171,16.867)--(6.21,16.899)--(6.245,16.932)--(6.275,16.966)--(6.301,17)--(6.322,17.035)--(6.339,17.07)--(6.351,17.106)--(6.358,17.141)--(6.36,17.177)--(6.358,17.213)--(6.351,17.249)--(6.339,17.284)--(6.323,17.32)--(6.302,17.354)--(6.277,17.389)--(6.247,17.423)--(6.212,17.456)--(6.174,17.488)--(6.131,17.52)--(6.084,17.55)--(6.033,17.58)--(5.978,17.609)--(5.919,17.636)--(5.857,17.662)--(5.792,17.687)--(5.723,17.71)--(5.652,17.732)--(5.577,17.753)--(5.5,17.772)--(5.421,17.789)--(5.339,17.805)--(5.256,17.819)--(5.17,17.832)--(5.083,17.842)--(4.995,17.851)--(4.906,17.858)--(4.816,17.863)--(4.726,17.866)--(4.635,17.868)--(4.544,17.868)--(4.453,17.865)--(4.363,17.861)--(4.273,17.855)--(4.184,17.847)--(4.097,17.838)--(4.011,17.826)--(3.926,17.813)--(3.843,17.798)--(3.763,17.782)--(3.684,17.764)--(3.608,17.744)--(3.535,17.723)--(3.465,17.7)--(3.398,17.676)--(3.334,17.651)--(3.273,17.624)--(3.216,17.596)--(3.163,17.567)--(3.114,17.537)--(3.068,17.506)--(3.027,17.474)--(2.991,17.441)--(2.958,17.408)--(2.93,17.374)--(2.907,17.339)--(2.888,17.304)--(2.874,17.269)--(2.864,17.233)--(2.859,17.197)--(2.859,17.161)--(2.864,17.126)--cycle;
          
          \\fill[color = ffhhhh, opacity = 0.2](2.887,17.055)--(2.905,17.02)--(2.929,16.985)--(2.956,16.951)--(2.989,16.917)--(3.025,16.885)--(3.066,16.853)--(3.111,16.821)--(3.16,16.791)--(3.213,16.762)--(3.27,16.734)--(3.33,16.707)--(3.394,16.682)--(3.461,16.658)--(3.531,16.635)--(3.604,16.614)--(3.68,16.594)--(3.758,16.576)--(3.839,16.559)--(3.921,16.544)--(4.006,16.531)--(4.092,16.519)--(4.179,16.51)--(4.268,16.502)--(4.358,16.496)--(4.448,16.492)--(4.539,16.489)--(4.629,16.489)--(4.72,16.49)--(4.811,16.493)--(4.901,16.498)--(4.99,16.505)--(5.078,16.514)--(5.165,16.524)--(5.251,16.537)--(5.334,16.55)--(5.416,16.566)--(5.496,16.583)--(5.573,16.602)--(5.647,16.623)--(5.719,16.645)--(5.788,16.668)--(5.854,16.693)--(5.916,16.719)--(5.975,16.746)--(6.03,16.775)--(6.081,16.805)--(6.128,16.835)--(6.171,16.867)--(6.21,16.899)--(6.245,16.932)--(6.275,16.966)--(6.301,17)--(6.322,17.035)--(6.339,17.07)--(6.351,17.106)--(6.358,17.141)--(6.36,17.177)--(6.358,17.213)--(6.351,17.249)--(6.339,17.284)--(6.323,17.32)--(6.302,17.354)--(6.277,17.389)--(6.247,17.423)--(6.212,17.456)--(6.174,17.488)--(6.131,17.52)--(6.084,17.55)--(6.033,17.58)--(5.978,17.609)--(5.919,17.636)--(5.857,17.662)--(5.792,17.687)--(5.723,17.71)--(5.652,17.732)--(5.577,17.753)--(5.5,17.772)--(5.421,17.789)--(5.339,17.805)--(5.256,17.819)--(5.17,17.832)--(5.083,17.842)--(4.995,17.851)--(4.906,17.858)--(4.816,17.863)--(4.726,17.866)--(4.635,17.868)--(4.544,17.868)--(4.453,17.865)--(4.363,17.861)--(4.273,17.855)--(4.184,17.847)--(4.097,17.838)--(4.011,17.826)--(3.926,17.813)--(3.843,17.798)--(3.763,17.782)--(3.684,17.764)--(3.608,17.744)--(3.535,17.723)--(3.465,17.7)--(3.398,17.676)--(3.334,17.651)--(3.273,17.624)--(3.216,17.596)--(3.163,17.567)--(3.114,17.537)--(3.068,17.506)--(3.027,17.474)--(2.991,17.441)--(2.958,17.408)--(2.93,17.374)--(2.907,17.339)--(2.888,17.304)--(2.874,17.269)--(2.864,17.233)--(2.859,17.197)--(2.859,17.161)--(2.864,17.126)(2.887,17.055);
          \\node at (3.922, 22.559) [align=left,below right ,black,,font= \\sf \\fontsize {0.469cm} {0.586cm} \\selectfont] {S};
          \\draw [color=black , dotted, line width = 0.4](4.609,21.776)--(8.987,10.281);
          \\draw [color=ofofof , dotted, line width = 0.4](4.609,17.178)--(6.36,17.178);
          \\draw [color=black , dotted, line width = 0.4](4.609,10.281)--(8.987,10.281);
          \\draw [color=black , dotted, line width = 0.4](4.609,10.281)--(4.609,21.776);
          \\draw [color=black , dotted, line width = 0.4](4.609,17.546)--(4.609,17.178);
          \\draw [color=black , dotted, line width = 0.4](4.609,17.178)--(5.009,17.178);
          \\draw [color=black , dotted, line width = 0.4](5.009,17.178)--(5.009,17.546);
          \\draw [color=black , dotted, line width = 0.4](5.009,17.546)--(4.609,17.546);
          \\draw [color=black , dotted, line width = 0.4](4.609,17.546)--(4.609,17.178)--(5.009,17.178)--(5.009,17.546)--(4.609,17.546)--cycle;
          \\draw [color=black , dotted, line width = 0.4](4.609,10.649)--(4.609,10.281);
          \\draw [color=black , dotted, line width = 0.4](4.609,10.281)--(5.009,10.281);
          \\draw [color=black , dotted, line width = 0.4](5.009,10.281)--(5.009,10.649);
          \\draw [color=black , dotted, line width = 0.4](5.009,10.649)--(4.609,10.649);
          \\draw [color=black , dotted, line width = 0.4](4.609,10.649)--(4.609,10.281)--(5.009,10.281)--(5.009,10.649)--(4.609,10.649)--cycle;
          \\end{tikzpicture} \n\t \\end{minipage}`
        }

        texteCorr = numAlpha(0) + ` L'aire de base du cône est : $\\pi \\times R^2$ cm${texteExposant(2)} $= \\pi \\times ${texNombre(r, 1)}^2$ cm${texteExposant(2)} $= ${texNombre(r.pow(2), 2)}\\pi$ cm${texteExposant(2)} $\\approx ${texNombre(r.pow(2).mul(pi).toDP(2), 2)}$ cm${texteExposant(2)}.<br>`
        texteCorr += numAlpha(1) + ` Le volume du cône est $\\dfrac{A_\\text{base}}{3}\\times \\text{hauteur}$ cm${texteExposant(3)} $= \\dfrac{${texNombre(r.pow(2), 2)}\\pi}{3} \\times ${texNombre(h1, 1)}$ cm${texteExposant(3)} $= \\dfrac{${texNombre(r.pow(2).mul(h1), 3)}}{3}\\pi$ cm${texteExposant(3)} $\\approx ${texNombre(r.pow(2).mul(h1).mul(pi).div(3), 2)}$ cm${texteExposant(3)}.<br>`
        texteCorr += numAlpha(2) + ` La section est une réduction de la base de coefficient $\\dfrac{${texNombre(h2, 1)}}{${texNombre(h1, 1)}}`
        if (!Number.isInteger(h1) || pgcd(h2, h1) > 1) { texteCorr += `=${texFractionReduite(h2.mul(10), h1.mul(10))}$.<br>` } else { texteCorr += '.$<br>' }
        texteCorr += `Dans une réduction de coefficient k, les aires sont multipliés par k${texteExposant(2)}.<br>`
        texteCorr += `Donc son aire est $\\left(${texFractionReduite(h2.mul(10), h1.mul(10))}\\right)^2 \\times ${texNombre(r.pow(2), 2)}\\pi$ cm${texteExposant(2)} $=${texFractionReduite(h2.mul(r).mul(10).pow(2), h1.mul(10).pow(2))}\\pi$ cm${texteExposant(2)} $\\approx${texNombre(h2.mul(r).div(h1).pow(2).mul(pi), 2)}$ cm${texteExposant(2)}.<br>`
        texteCorr += numAlpha(3) + ` Dans une réduction de coefficient k, les volumes sont multipliés par k${texteExposant(3)}.<br>`
        texteCorr += `Donc le volume du cône de hauteur SO' est : $\\left(${texFractionReduite(h2.mul(10), h1.mul(10))}\\right)^3 \\times \\dfrac{${texNombre(r.mul(r).mul(h1), 3)}}{3}\\pi$ cm${texteExposant(3)} $\\approx ${texNombre(h2.pow(3).mul(r.pow(2)).mul(pi).div(h1.pow(2)).div(3), 2)}$ cm${texteExposant(3)} '.<br>`
        texteCorr += numAlpha(4) + ' Le volume du tronc de cône est : '
        texteCorr += `$V_\\text{Cône} - V_\\text{CôneRéduit}$<br>Soit : <br>$\\dfrac{${texNombre(r.pow(2).mul(h1), 3)}}{3}\\pi$ cm${texteExposant(3)}$ - \\left(${texFractionReduite(h2.mul(10), h1.mul(10))}\\right)^3 \\times \\dfrac{${texNombre(r.pow(2).mul(h1), 3)}}{3}\\pi$ cm${texteExposant(3)} `
        texteCorr += `$ = \\left(1-\\left(${texFractionReduite(h2.mul(10), h1.mul(10))}\\right)^3\\right)\\times \\dfrac{${texNombre(r.pow(2).mul(h1))}}{3}\\pi$ cm${texteExposant(3)} `
        texteCorr += `$ = \\left(1-\\dfrac{${fractionSimplifiee(h2.mul(10), h1.mul(10))[0] ** 3}}{${fractionSimplifiee(h2.mul(10), h1.mul(10))[1] ** 3}}\\right)\\times \\dfrac{${texNombre(r.pow(2).mul(h1), 3)}}{3}\\pi$ cm${texteExposant(3)} `
        texteCorr += `$ = \\dfrac{${fractionSimplifiee(h2.mul(10), h1.mul(10))[1] ** 3 - fractionSimplifiee(h2.mul(10), h1.mul(10))[0] ** 3}}{${fractionSimplifiee(h2.mul(10), h1.mul(10))[1] ** 3}}\\times \\dfrac{${texNombre(r.pow(2).mul(h1), 3)}}{3}\\pi$ cm${texteExposant(3)} `
        texteCorr += `$ \\approx ${texNombre((fractionSimplifiee(h2.mul(10), h1.mul(10))[1] ** 3 - fractionSimplifiee(h2.mul(10), h1.mul(10))[0] ** 3) * r.pow(2).mul(h1).mul(pi).div(fractionSimplifiee(h2.mul(10), h1.mul(10))[1] ** 3 * 3), 3)}$ cm${texteExposant(3)}<br>`
        this.MG32codeBase64 = codeBase64
        this.mg32init = (mtg32App, idDoc) => {
          mtg32App.giveFormula2(idDoc, 'r', r.toString())
          mtg32App.giveFormula2(idDoc, 'h1', h1.toString())
          mtg32App.giveFormula2(idDoc, 'h2', h2.toString())
          mtg32App.calculate(idDoc, true)
          return mtg32App.display(idDoc)
        }
        break
      case 3: // calcul de l'aire de base, du volume d'une pyramide à base triangulaire. puis, calcul de la section, du volume de la petite pyramide et du volume du tronc
        c = new Decimal(randint(30, 60)).div(10)
        c2 = new Decimal(randint(30, 60)).div(10)
        h1 = new Decimal(randint(12, 20) / 2)
        h2 = new Decimal(randint(3, h1.floor().sub(1)))
        if (this.sup2 < 3) {
          if (parseInt(this.sup2) === 1) { // coefficient de réduction décimal
            while (!h2.div(h1).mul(10).eq(h2.div(h1).mul(10).round())) {
              c = new Decimal(randint(30, 60)).div(10)
              c2 = new Decimal(randint(30, 60)).div(10)
              h1 = new Decimal(randint(12, 20) / 2)
              h2 = new Decimal(randint(3, h1.floor().sub(1)))
            }
          } else { // coefficient de réduction rationnel
            while (h2.div(h1).mul(10).eq(h2.div(h1).mul(10).round())) {
              c = new Decimal(randint(30, 60)).div(10)
              c2 = new Decimal(randint(30, 60)).div(10)
              h1 = new Decimal(randint(12, 20) / 2)
              h2 = new Decimal(randint(3, h1.floor().sub(1)))
            }
          }
        }
        codeBase64 = 'TWF0aEdyYXBoSmF2YTEuMAAAABI+TMzNAANmcmH###8BAP8BAAAAAAAAAAAFHAAAAtIAAAAAAAAAAAAAAAEAAAEg#####wAAAAEACkNDYWxjQ29uc3QA#####wACcGkAFjMuMTQxNTkyNjUzNTg5NzkzMjM4NDb#####AAAAAQAKQ0NvbnN0YW50ZUAJIftURC0Y#####wAAAAEACkNQb2ludEJhc2UA#####wAAAAAAEAAAAEAIAAAAAAAAAAAAAAAAAAAFAAFAf2gAAAAAAEB5uFHrhR64#####wAAAAEAB0NDYWxjdWwA#####wAFbWluaTEAAzAuMgAAAAE#yZmZmZmZmgAAAAMA#####wAFbWF4aTEAATMAAAABQAgAAAAAAAD#####AAAAAQAUQ0ltcGxlbWVudGF0aW9uUHJvdG8A#####wAHQ3Vyc2V1cgAAAAUAAAAFAAAAAwAAAAIAAAADAAAAAf####8AAAABABRDRHJvaXRlRGlyZWN0aW9uRml4ZQAAAAAEAQAAAAAQAAABAAEAAAABAT#wAAAAAAAA#####wAAAAEAD0NQb2ludExpZURyb2l0ZQEAAAAEAAAAAAAQAAAAwAgAAAAAAAA#8AAAAAAAAAUAAUBMgAAAAAAAAAAABf####8AAAABAAtDSG9tb3RoZXRpZQAAAAAEAAAAAf####8AAAABAApDT3BlcmF0aW9uA#####8AAAABAA9DUmVzdWx0YXRWYWxldXIAAAACAAAACAEAAAAJAAAAAgAAAAkAAAAD#####wAAAAEAC0NQb2ludEltYWdlAAAAAAQBAAAAAA0AAk82AMAQAAAAAAAAQBAAAAAAAAAFAAAAAAYAAAAHAAAABwAAAAAEAAAAAQAAAAgDAAAACAEAAAABP#AAAAAAAAAAAAAJAAAAAgAAAAgBAAAACQAAAAMAAAAJAAAAAgAAAAoAAAAABAEAAAAADQACSTUAwAAAAAAAAABACAAAAAAAAAUAAAAABgAAAAn#####AAAAAQAIQ1NlZ21lbnQBAAAABAAAAAAAEAAAAQEBAAAAAQAAAAYAAAAGAQAAAAQAAAAAARAAAmsxAMAAAAAAAAAAQAAAAAAAAAABAAE#0xZ0xZ0xZwAAAAv#####AAAAAgAPQ01lc3VyZUFic2Npc3NlAQAAAAQABHpvb20AAAAIAAAACgAAAAz#####AAAAAQAPQ1ZhbGV1ckFmZmljaGVlAQAAAAQBAAAAAAAAAAAAAAAAwBgAAAAAAAAAAAAMDwAB####AAAAAQAAAAIAAAABAAAAAAAAAAAAAAAAAgAAAA0AAAADAP####8AAmMnAAE0AAAAAUAQAAAAAAAAAAAAAwD#####AAJoMQACMTAAAAABQCQAAAAAAAAAAAADAP####8AAmgyAAE0AAAAAUAQAAAAAAAAAAAAAwD#####AAJoMwAFaDEtaDIAAAAIAQAAAAkAAAAQAAAACQAAABEAAAADAP####8AAWMAATMAAAABQAgAAAAAAAAAAAACAP####8AAAAAAA8AAU8AwCgAAAAAAABAEAAAAAAAAAUAAUBrEAAAAAAAQH3YUeuFHrgAAAAFAP####8BAAAAABAAAAEAAQAAABQBP#MzMzMzMzMAAAACAP####8BAAAAAQ8AAk8yAQUAAUCBFAAAAAAAQGPQo9cKPXEAAAACAP####8BAAAAAQ8AAk8zAQUAAUCBJAAAAAAAQG3wo9cKPXEAAAAFAP####8BAAAAABAAAAEAAQAAABcBP#MzMzMzMzMAAAACAP####8BAAAAAQ8AAk80AQUAAUCBHAAAAAAAQHS4UeuFHrgAAAAFAP####8BAAAAABAAAAEAAQAAABkBP#MzMzMzMzMAAAAFAP####8BAAAAARAAAAEAAQAAABYAP#AAAAAAAAAAAAAGAP####8BAAAAAQ8AAkoyAQUAAMBCAAAAAAAAAAAAG#####8AAAABAAlDQ2VyY2xlT0EA#####wB#f38BAQAAABYAAAAc#####wAAAAEADENUcmFuc2xhdGlvbgD#####AAAAFgAAABwAAAAKAP####8BAAAAABAAAAEFAAAAABcAAAAeAAAADgD#####AH9#fwEBAAAAFwAAAB######AAAAAQAQQ0ludERyb2l0ZUNlcmNsZQD#####AAAAGAAAACD#####AAAAAQAQQ1BvaW50TGllQmlwb2ludAD#####AQAAAAENAAJJMwEFAAEAAAAh#####wAAAAEAD0NQb2ludExpZUNlcmNsZQD#####AAAAAAEPAAJLMgEBAAFAAGSoGqf0lgAAAB0AAAASAP####8AAAAAAQ8AAkszAQEAAUAWHME9jCZzAAAAIAAAAAsA#####wAAAAAAEAAAAQABAAAAFgAAABwAAAALAP####8AAAAAABAAAAEAAQAAABYAAAAjAAAACwD#####AAAAAAAQAAABAAEAAAAXAAAAIgAAAAsA#####wAAAAAAEAAAAQABAAAAFwAAACT#####AAAAAgATQ01lc3VyZUFuZ2xlT3JpZW50ZQD#####AAZhbmdwaGkAAAAcAAAAFgAAACMAAAATAP####8AB2FuZ3RldGEAAAAiAAAAFwAAACQAAAADAP####8AA3BoaQAGYW5ncGhpAAAACQAAACkAAAADAP####8ABXRoZXRhAAdhbmd0ZXRhAAAACQAAACoAAAAHAP####8AAAAZ#####wAAAAIACUNGb25jdGlvbgQAAAAJAAAAKwAAAAMA#####wADeCcxAApzaW4odGhldGEpAAAAFAMAAAAJAAAALAAAAAMA#####wADeScxABQtY29zKHRoZXRhKSpzaW4ocGhpKQAAAAgBAAAAAQAAAAAAAAAAAAAACAIAAAAUBAAAAAkAAAAsAAAAFAMAAAAJAAAAKwAAAAMA#####wADeCcyAApjb3ModGhldGEpAAAAFAQAAAAJAAAALAAAAAMA#####wADeScyABNzaW4odGhldGEpKnNpbihwaGkpAAAACAIAAAAUAwAAAAkAAAAsAAAAFAMAAAAJAAAAK#####8AAAACABNDTWFycXVlQW5nbGVPcmllbnRlAP####8AAAD#AAIAAAAAQDzMlF2JcmgAAAAcAAAAFgAAACMB#####wAAAAEADENCaXNzZWN0cmljZQD#####AQAA#wAQAAABAQEAAAAcAAAAFgAAACMAAAAGAP####8BAAD#ABAAAAEFAAFAgM#j0J2QXQAAADP#####AAAAAgAGQ0xhdGV4AP####8AAAD#AMAQAAAAAAAAwBQAAAAAAAAAAAA0EQAAAAAAAAAAAAAAAAABAAAAAAAAAAAAB1x2YXJwaGkAAAAVAP####8AfwAAAAIAAAAAQDxTDia4t4kAAAAiAAAAFwAAACQBAAAAFgD#####AX8AAAAQAAABAQEAAAAiAAAAFwAAACQAAAAGAP####8BfwAAABAAAAEFAAFAfSZmyCoB2wAAADcAAAAXAP####8AfwAAAMAUAAAAAAAAwCYAAAAAAAAAAAA4EQAAAAAAAAAAAAAAAAABAAAAAAAAAAAAClx2YXJ0aGV0YSAAAAAFAP####8BAAAAARAAAAEAAQAAABkAP#AAAAAAAAAAAAAGAP####8AAAAAAQ8AAko0AQUAAcBGLhR64UewAAAAOgAAAA4A#####wBmZmYAAQAAABkAAAA7AAAAEgD#####AQAAAAAQAAABBQABP#CX6bp5AmEAAAA8AAAABQD#####AQAAAAAQAAABAAEAAAA9AD#zMzMzMzMz#####wAAAAEAEENJbnREcm9pdGVEcm9pdGUA#####wEAAAAAEAAAAQUAAAAAGgAAAD4AAAAQAP####8AAAAaAAAAPAAAABEA#####wEAAAABDQACSTQBBQABAAAAQP####8AAAACAAdDUmVwZXJlAP####8AAAAAAQEAAAAZAAAAQQAAADsAAAAAAAABAAAAAAAAAAAAAAABAAAAAAAAAAAAAAABP#AAAAAAAAAAAAABP#AAAAAAAAAAAAAKAP####8BAAAAABAAAAEFAAAAADsAAAAtAAAABwD#####AAAAPwAAABQEAAAACQAAACsAAAAKAP####8BAAAAABAAAAEFAAAAAD0AAABE#####wAAAAIADUNMaWV1RGVQb2ludHMA#####wAAf38BAQAAAEUAAABkAAAAAAA9AAAABQAAAD0AAAA+AAAAPwAAAEQAAABF#####wAAAAEACENWZWN0ZXVyAP####8AAAD#ABAAAAEAAQAAABkAAABDAP####8AAAABABBDUG9pbnREYW5zUmVwZXJlAP####8BAAAAABAAAAEFAAAAAEIAAAAJAAAALgAAAAkAAAAvAAAAHAD#####AQAAAAAQAAABBQAAAABCAAAACQAAADAAAAAJAAAAMQAAABsA#####wD#AAAAEAAAAQABAAAAGQAAAEgAAAAAGwD#####AAB#AAAQAAABAAEAAAAZAAAASQAAAAAaAP####8AZmZmAQEAAABIAAAAZAAAAAAAJAAAAAYAAAAkAAAAKgAAACwAAAAuAAAALwAAAEj#####AAAAAQAMQ1N1cmZhY2VMaWV1AP####8Af39#AAAABQAAAEwAAAAdAP####8Af39#AAAABQAAAEYAAAACAP####8BAAAAAA8AAVoAAAAAAAAAAABACAAAAAAAAAUAAUB2qAAAAAAAQFEhR64UeuIAAAAFAP####8BAAAAARAAAAEBAQAAAE8BP#AAAAAAAAAAAAAPAP####8AAAAXAAAAIgAAAAoA#####wEAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAAE8AAABR#####wAAAAEADUNEZW1pRHJvaXRlT0EA#####wH#AAAADQAAAQEBAAAATwAAAFIAAAAFAP####8B#wAAARAAAAEAAQAAAE8AP#AAAAAAAAD#####AAAAAQALQ1NpbWlsaXR1ZGUA#####wAAAE8AAAABQFaAAAAAAAAAAAABP9MzMzMzMzMAAAAKAP####8B#wAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAABSAAAAVQAAAB8A#####wAAAE######AAAAAQAMQ01vaW5zVW5haXJlAAAAAUBWgAAAAAAAAAAAAT#TMzMzMzMzAAAACgD#####Af8AAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAAUgAAAFcAAAALAP####8B#wAAABAAAAEAAQAAAFYAAABY#####wAAAAIADENDb21tZW50YWlyZQD#####AP8AAAH#####EEB#qAAAAAAAQHpoUeuFHrgCAAAAAAAAAAAAAAAAAQAAAAAAAAAAAARaT09N#####wAAAAEABUNGb25jAP####8ABHplcm8ADWFicyh0KTwwLjAwMDEAAAAIBAAAABQA#####wAAAAIAEUNWYXJpYWJsZUZvcm1lbGxlAAAAAAAAAAE#Gjbi6xxDLQABdAAAAAcA#####wAAABQAAAABP+AAAAAAAAAAAAAHAP####8AAABPAAAACQAAAA0AAAAKAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAABSAAAAXf####8AAAABAA5DUG9pbnRMaWVQb2ludAD#####Af8AAAAPAAFVAMAQAAAAAAAAwDcAAAAAAAIFAAAAAF7#####AAAAAQAJQ0xvbmd1ZXVyAP####8AAABPAAAAX#####8AAAACAAlDQ2VyY2xlT1IA#####wEAAAABAQAAABQAAAABP#AAAAAAAAAAAAAAEAD#####AAAAFQAAAGEAAAARAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQACAAAAYgAAABEA#####wEAAAAADwACSTIAAAAAAAAAAABACAAAAAAAAAUAAQAAAGIAAAAkAP####8BAAAAAAsAAkkxAMAQAAAAAAAAQBAAAAAAAAAFAAAAAGT#####AAAAAQAJQ0Ryb2l0ZUFCAP####8BAAAAAA0AAAEAAQAAABQAAABl#####wAAAAEAFkNEcm9pdGVQZXJwZW5kaWN1bGFpcmUA#####wEAAAAAEAAAAQABAAAAFAAAAGYAAAAOAP####8BAAAAAAEAAAAUAAAAZQAAABAA#####wAAAGcAAABoAAAAEQD#####AQAAAAALAAJKMQDAKAAAAAAAAMAQAAAAAAAABQACAAAAaQAAABkA#####wCAgIABAQAAABQAAABlAAAAagAAAAAAAAEAAAAAAAAAAAAAAAEAAAAAAAAAAAAAAAE#8AAAAAAAAAAAAAE#8AAAAAAAAAAAABwA#####wEAAAAADwABSwBAEAAAAAAAAMA3AAAAAAAABQAAAABrAAAAAQAAAAAAAAAAAAAAFAQAAAAJAAAAKwAAABwA#####wEAAAAADwABSQDAEAAAAAAAAD#wAAAAAAAABQAAAABrAAAACQAAAC4AAAAJAAAALwAAABwA#####wEAAAAADwABSgEFAAAAAGsAAAAJAAAAMAAAAAkAAAAxAAAAHgD#####AQAAAAANAAABAQEAAAAUAAAAbQAAAB4A#####wEAAAAADQAAAQEBAAAAFAAAAG4AAAAeAP####8BAAAAAA0AAAEBAQAAABQAAABsAAAAGwD#####Af8AAAAQAAABAAEAAAAUAAAAbQAAAAAbAP####8BAH8AABAAAAEAAQAAABQAAABuAAAAABsA#####wEAAP8AEAAAAQABAAAAFAAAAGwA#####wAAAAEAEUNQb2ludFBhckFic2Npc3NlAP####8BAAAAAA8AAUEAAAAAAAAAAABACAAAAAAAAAUAAAAAFAAAAG0AAAAJAAAAEwAAACkA#####wEAAAAADwABQgAAAAAAAAAAAEAIAAAAAAAABQAAAAAUAAAAbgAAAAkAAAAPAAAAKQD#####AQAAAAAPAAFTAAAAAAAAAAAAQAgAAAAAAAAFAAAAABQAAABsAAAACQAAABAAAAApAP####8AAAAAAA8AAk8nAAAAAAAAAAAAQAgAAAAAAAAFAAAAABQAAABsAAAACQAAABIAAAALAP####8AAAAAABAAAAEBAQAAAHUAAAAUAAAACwD#####AAAAAAAQAAABAQEAAAAUAAAAdgAAAAsA#####wAAAAAAEAAAAQEBAAAAdgAAAHUAAAALAP####8AAAAAABAAAAEBAQAAAHcAAAB1AAAACwD#####AAAAAAAQAAABAQEAAAB3AAAAdgAAAAcA#####wAAAHcAAAAIAwAAAAkAAAARAAAACQAAABAAAAAKAP####8BAAAAAA8AAkEnAAAAAAAAAAAAQAgAAAAAAAAFAAAAAHUAAAB+AAAACgD#####AQAAAAAPAAJCJwAAAAAAAAAAAEAIAAAAAAAABQAAAAB2AAAAfgAAAAsA#####wAAAAAAEAAAAQEBAAAAfwAAAHgAAAALAP####8AAAAAABAAAAEBAQAAAHgAAACAAAAACwD#####AAAAAAAQAAABAQEAAAB#AAAAgAAAAAQA#####wAXTWVzdXJlIGQnYW5nbGUgb3JpZW50w6kAAAACAAAAAQAAAAMAAAB2AAAAdQAAABQAAAAWAAAAAIQBAAAAABAAAAEAAQAAABQAAAB1AAAAdgAAAAYAAAAAhAEAAAAAEAAAAAAAAAAAAAAAP+MzMzMzMzMFAAFAaT5Clg7dyQAAAIUAAAATAQAAAIQABGFuZzEAAAB2AAAAdQAAABQAAAAEAP####8AF01lc3VyZSBkJ2FuZ2xlIG9yaWVudMOpAAAAAgAAAAEAAAADAAAAFAAAAHUAAAB3AAAAFgAAAACIAQAAAAAQAAABAAEAAAB3AAAAdQAAABQAAAAGAAAAAIgBAAAAABAAAAAAAAAAAAAAAD#jMzMzMzMzBQABQGk+QpYO3ckAAACJAAAAEwEAAACIAARhbmcyAAAAFAAAAHUAAAB3AAAABAD#####ABdNZXN1cmUgZCdhbmdsZSBvcmllbnTDqQAAAAIAAAABAAAAAwAAAHcAAAB1AAAAdgAAABYAAAAAjAEAAAAAEAAAAQABAAAAdgAAAHUAAAB3AAAABgAAAACMAQAAAAAQAAAAAAAAAAAAAAA#4zMzMzMzMwUAAUBpPkKWDt3JAAAAjQAAABMBAAAAjAAEYW5nMwAAAHcAAAB1AAAAdgAAAAMA#####wAEc29tQQAOYW5nMSthbmcyK2FuZzMAAAAIAAAAAAgAAAAACQAAAIcAAAAJAAAAiwAAAAkAAACPAAAAAwD#####AAlTQXZpc2libGUADDEvemVybyhzb21BKQAAAAgDAAAAAT#wAAAAAAAA#####wAAAAEADkNBcHBlbEZvbmN0aW9uAAAAWwAAAAkAAACQAAAABwD#####AAAAdwAAAAkAAACRAAAACgD#####Af8AAAANAAJBMQAAAAAAAAAAAEAIAAAAAAAABQAAAAB1AAAAkgAAAAsA#####wAAAAAAEAAAAQACAAAAdwAAAJMAAAAEAP####8AF01lc3VyZSBkJ2FuZ2xlIG9yaWVudMOpAAAAAgAAAAEAAAADAAAAdwAAAHYAAAAUAAAAFgAAAACVAQAAAAAQAAABAAEAAAAUAAAAdgAAAHcAAAAGAAAAAJUBAAAAABAAAAAAAAAAAAAAAD#jMzMzMzMzBQABQGk+QpYO3ckAAACWAAAAEwEAAACVAARhbmc0AAAAdwAAAHYAAAAUAAAABAD#####ABdNZXN1cmUgZCdhbmdsZSBvcmllbnTDqQAAAAIAAAABAAAAAwAAAHUAAAB2AAAAdwAAABYAAAAAmQEAAAAAEAAAAQABAAAAdwAAAHYAAAB1AAAABgAAAACZAQAAAAAQAAAAAAAAAAAAAAA#4zMzMzMzMwUAAUBpPkKWDt3JAAAAmgAAABMBAAAAmQAEYW5nNQAAAHUAAAB2AAAAdwAAAAQA#####wAXTWVzdXJlIGQnYW5nbGUgb3JpZW50w6kAAAACAAAAAQAAAAMAAAAUAAAAdgAAAHUAAAAWAAAAAJ0BAAAAABAAAAEAAQAAAHUAAAB2AAAAFAAAAAYAAAAAnQEAAAAAEAAAAAAAAAAAAAAAP+MzMzMzMzMFAAFAaT5Clg7dyQAAAJ4AAAATAQAAAJ0ABGFuZzYAAAAUAAAAdgAAAHUAAAADAP####8ABHNvbUIADmFuZzQrYW5nNSthbmc2AAAACAAAAAAIAAAAAAkAAACYAAAACQAAAJwAAAAJAAAAoAAAAAMA#####wAJU0J2aXNpYmxlAAwxL3plcm8oc29tQikAAAAIAwAAAAE#8AAAAAAAAAAAACoAAABbAAAACQAAAKEAAAAHAP####8AAAB3AAAACQAAAKIAAAAKAP####8BAAAAAA0AAkIxAAAAAAAAAAAAQAgAAAAAAAAFAAAAAHYAAACjAAAACwD#####AAAAAAAQAAABAAIAAAB3AAAApAAAAAQA#####wAXTWVzdXJlIGQnYW5nbGUgb3JpZW50w6kAAAACAAAAAQAAAAMAAAB3AAAAFAAAAHUAAAAWAAAAAKYBAAAAABAAAAEAAQAAAHUAAAAUAAAAdwAAAAYAAAAApgEAAAAAEAAAAAAAAAAAAAAAP+MzMzMzMzMFAAFAaT5Clg7dyQAAAKcAAAATAQAAAKYABGFuZzcAAAB3AAAAFAAAAHUAAAAEAP####8AF01lc3VyZSBkJ2FuZ2xlIG9yaWVudMOpAAAAAgAAAAEAAAADAAAAdQAAABQAAAB2AAAAFgAAAACqAQAAAAAQAAABAAEAAAB2AAAAFAAAAHUAAAAGAAAAAKoBAAAAABAAAAAAAAAAAAAAAD#jMzMzMzMzBQABQGk+QpYO3ckAAACrAAAAEwEAAACqAARhbmc4AAAAdQAAABQAAAB2AAAABAD#####ABdNZXN1cmUgZCdhbmdsZSBvcmllbnTDqQAAAAIAAAABAAAAAwAAAHYAAAAUAAAAdwAAABYAAAAArgEAAAAAEAAAAQABAAAAdwAAABQAAAB2AAAABgAAAACuAQAAAAAQAAAAAAAAAAAAAAA#4zMzMzMzMwUAAUBpPkKWDt3JAAAArwAAABMBAAAArgAFYW5nMTAAAAB2AAAAFAAAAHcAAAADAP####8ABHNvbU8AD2FuZzcrYW5nOCthbmcxMAAAAAgAAAAACAAAAAAJAAAAqQAAAAkAAACtAAAACQAAALEAAAADAP####8ACVNPdmlzaWJsZQAMMS96ZXJvKHNvbU8pAAAACAMAAAABP#AAAAAAAAAAAAAqAAAAWwAAAAkAAACyAAAABwD#####AAAAdwAAAAkAAACzAAAACgD#####AQAAAAANAAJPMQAAAAAAAAAAAEAIAAAAAAAABQAAAAAUAAAAtAAAAAsA#####wAAAAAAEAAAAQACAAAAdwAAALUAAAAnAP####8BAAAAABAAAAEAAQAAAHYAAAAUAAAAJwD#####AQAAAAAQAAABAAEAAAB1AAAAFAAAACcA#####wEAAAAAEAAAAQABAAAAdgAAAHUAAAALAP####8AAAAAABAAAAEBAQAAAHcAAAAUAAAAGAD#####AQAAAAAQAAJ3MQAAAAAAAAAAAEAIAAAAAAAABQAAAAC4AAAAfQAAAAwA#####wAEYWJzMQAAAHYAAAB3AAAAu#####8AAAABAA5DVGVzdEV4aXN0ZW5jZQD#####AAZ0ZXN0T0EAAAC8AAAAAwD#####AAlPQXZpc2libGUADDEvKDEtdGVzdE9BKQAAAAgDAAAAAT#wAAAAAAAAAAAACAEAAAABP#AAAAAAAAAAAAAJAAAAvQAAABgA#####wEAAAAAEAACdzIAAAAAAAAAAABACAAAAAAAAAUAAAAAtgAAALkAAAAMAP####8ABGFiczIAAAAUAAAAdwAAAL8AAAArAP####8ABnRlc3RBQgAAAMAAAAADAP####8ACUFCdmlzaWJsZQAMMS8oMS10ZXN0QUIpAAAACAMAAAABP#AAAAAAAAAAAAAIAQAAAAE#8AAAAAAAAAAAAAkAAADBAAAAGAD#####AQAAAAAQAAJ3MwAAAAAAAAAAAEAIAAAAAAAABQAAAAB8AAAAtwAAAAwA#####wAEYWJzMwAAAHUAAAB3AAAAwwAAACsA#####wAGdGVzdE9CAAAAxAAAAAMA#####wAJT0J2aXNpYmxlAAwxLygxLXRlc3RPQikAAAAIAwAAAAE#8AAAAAAAAAAAAAgBAAAAAT#wAAAAAAAAAAAACQAAAMUAAAAHAP####8AAAB3AAAACQAAAL4AAAAKAP####8BAAAAABAAAkEyAAAAAAAAAAAAQAgAAAAAAAAFAAAAAHUAAADHAAAACwD#####AAAAAAAQAAABAAIAAADIAAAAFAAAAAcA#####wAAAHcAAAAJAAAAwgAAAAoA#####wEAAAAAEAACQjIAAAAAAAAAAABACAAAAAAAAAUAAAAAdgAAAMoAAAALAP####8BAAAAABAAAAEAAgAAAMsAAAB1AAAABwD#####AAAAdwAAAAkAAADGAAAACgD#####AQAAAAAQAAJCMwAAAAAAAAAAAEAIAAAAAAAABQAAAAB2AAAAzQAAAAsA#####wAAAAAAEAAAAQACAAAAzgAAABQAAAAKAP####8BAAAAABAAAkE0AAAAAAAAAAAAQAgAAAAAAAAFAAAAAH8AAADKAAAACwD#####AAAAAAAQAAABAAIAAADQAAAAgAAAAAoA#####wEAAAAAEAACQjQAAAAAAAAAAABACAAAAAAAAAUAAAAAgAAAAM0AAAALAP####8AAAAAABAAAAEAAgAAANIAAAB4AAAACgD#####AQAAAAAQAAJPNQAAAAAAAAAAAEAIAAAAAAAABQAAAAB4AAAAxwAAAAsA#####wAAAAAAEAAAAQACAAAA1AAAAH######AAAAAQAOQ0NlbnRyZUdyYXZpdGUA#####wEAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAAH8AAAB4AAAAgAAAAAcA#####wAAANYAAAABP#TMzMzMzM0AAAAKAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAAB#AAAA1wAAAAoA#####wEAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAAHgAAADXAAAACgD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAAgAAAANcAAAAhAP####8AAAAAAMAkAAAAAAAAwCQAAAAAAAAAAADYEAAAAAAAAAAAAAAAAAABAAAAAAAAAAAABCNHQScAAAAhAP####8AAAAAAMAAAAAAAAAAwBgAAAAAAAAAAADaEAAAAAAAAAAAAAAAAAABAAAAAAAAAAAABCNHQicAAAAhAP####8AAAAAAD#wAAAAAAAAwDEAAAAAAAAAAADZEAAAAAAAAAAAAAAAAAABAAAAAAAAAAAABCNHTycAAAAsAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAAB1AAAAFAAAAHYAAAAHAP####8AAADeAAAAAT#zMzMzMzMzAAAACgD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAAdQAAAN8AAAAKAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAAB2AAAA3wAAAAoA#####wEAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAABQAAADfAAAAIQD#####AAAAAADAOQAAAAAAAMAoAAAAAAAAAAAAdRAAAAAAAAAAAAAAAAAAAQAAAAAAAAAAAAMjR0EAAAAhAP####8AAAAAAMAQAAAAAAAAwCAAAAAAAAAAAADhEAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAyNHQgAAACEA#####wAAAAAAwBgAAAAAAADAIgAAAAAAAAAAAOIQAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAADI0dPAAAACgD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAAbgAAAFwAAAAKAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAABtAAAAXAAAAAsA#####wB#f38AEAAAAQEBAAAAFAAAAOYAAAAPAP####8AAAAUAAAA5wAAAAsA#####wB#f38AEAAAAQEBAAAA5wAAABQAAAAPAP####8AAAAUAAAA5gAAAAoA#####wF#f38AEAAAAEAIAAAAAAAAAAAAAAAAAAAFAAAAAOcAAADrAAAACwD#####AH9#fwAQAAABAQEAAADnAAAA7AAAAAsA#####wB#f38AEAAAAQEBAAAA7AAAAOb#####AAAAAQAJQ1BvbHlnb25lAP####8Af39#AQEAAAAFAAAA5gAAABQAAADnAAAA7AAAAOYAAAAKAP####8Bf39#ABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAAB4AAAA6wAAAAoA#####wF#f38AEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAAHgAAADpAAAACwD#####AH9#fwAQAAABAQEAAAB4AAAA8AAAAA8A#####wAAAHgAAADxAAAACwD#####AH9#fwAQAAABAQEAAADxAAAAeAAAAA8A#####wAAAHgAAADwAAAACgD#####AX9#fwAQAAAAQAgAAAAAAAAAAAAAAAAAAAUAAAAA8QAAAPUAAAALAP####8Af39#ABAAAAEBAQAAAPEAAAD2AAAACwD#####AH9#fwAQAAABAQEAAAD2AAAA8AAAAC0A#####wB#f38BAQAAAAUAAADwAAAAeAAAAPEAAAD2AAAA8AAAAAoA#####wF#f38AEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAAGwAAABcAAAADwD#####AAAAFAAAAPoAAAAKAP####8Bf39#ABAAAABACAAAAAAAAAAAAAAAAAAABQAAAADmAAAA+wAAAAsA#####wB#f38AEAAAAQEBAAAA+gAAABQAAAALAP####8Af39#ABAAAAEBAQAAAOYAAAD8AAAACwD#####AH9#fwAQAAABAQEAAAD8AAAA+gAAAC0A#####wB#f38BAQAAAAUAAAD6AAAAFAAAAOYAAAD8AAAA+gAAAA8A#####wAAABQAAADnAAAACgD#####AX9#fwAQAAAAQAgAAAAAAAAAAAAAAAAAAAUAAAAA+gAAAQEAAAALAP####8Af39#ABAAAAEBAQAAAPoAAAECAAAACwD#####AH9#fwAQAAABAQEAAAECAAAA5wAAAC0A#####wB#f38BAQAAAAUAAADnAAAAFAAAAPoAAAECAAAA5wAAAAoA#####wF#f38AEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAAHgAAAD7AAAADwD#####AAAAeAAAAQYAAAAKAP####8Bf39#ABAAAABACAAAAAAAAAAAAAAAAAAABQAAAADwAAABBwAAAAsA#####wB#f38AEAAAAQEBAAABBgAAAHgAAAALAP####8Af39#ABAAAAEBAQAAAPAAAAEIAAAACwD#####AH9#fwAQAAABAQEAAAEIAAABBgAAAC0A#####wB#f38BAQAAAAUAAAEGAAAAeAAAAPAAAAEIAAABBgAAAA8A#####wAAAHgAAADxAAAACgD#####AX9#fwAQAAAAQAgAAAAAAAAAAAAAAAAAAAUAAAABBgAAAQ0AAAALAP####8Af39#ABAAAAEBAQAAAQYAAAEOAAAACwD#####AH9#fwAQAAABAQEAAAEOAAAA8QAAAC0A#####wB#f38BAQAAAAUAAADxAAAAeAAAAQYAAAEOAAAA8QAAAC0A#####wD#AAABAQAAAAQAAAB#AAAAgAAAAHgAAAB######wAAAAEAEENTdXJmYWNlUG9seWdvbmUA#####wD#AAAAAAAFAAABEgAAAC0A#####wAAfwABAQAAAAQAAAB1AAAAdgAAABQAAAB1AAAALgD#####AAAA#wAAAAUAAAEUAAAACgD#####AQAA#wAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAAdwAAAPsAAAAhAP####8AAAAAAMAwAAAAAAAAwCIAAAAAAAAAAAEWEAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAyNHUwAAACkA#####wEAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAAHgAAAB3AAAAAT#TMzMzMzMzAAAAKQD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAAFAAAAHgAAAABP9mZmZmZmZoAAAANAP####8AAAAAAMAoAAAAAAAAwB#######+AAAAEYEAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAQAAABEAAAANAP####8AAAAAAMAuAAAAAAAAwCAAAAAAAAAAAAEZEAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAQAAABIAAAApAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAAB1AAAAFAAAAAE#2ZmZmZmZmgAAACkA#####wEAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAABQAAAB2AAAAAT#jMzMzMzMzAAAADQD#####AAAAAADAHAAAAAAAAMA2AAAAAAAAAAABHBAAAAAAAAAAAAAAAAAAAQAAAAAAAAAAAAAAAAIAAAATAAAADQD#####AAAAAAC#8AAAAAAAAMAzAAAAAAAAAAABHRAAAAAAAAAAAAAAAAAAAQAAAAAAAAAAAAAAAAIAAAAPAAAAYP##########'
        if (!context.isHtml) { texte = '\\begin{minipage}{0.7 \\linewidth} \n\t' } else { texte = '' }
        texte += `SOAB est une pyramide à base triangulaire de hauteur $SO${sp()}=${sp()}${texNombre(h1, 1)}${sp()}$cm.<br> Sa base est un triangle OAB rectangle en O tel que $OA${sp()}=${sp()}${texNombre(c, 1)}${sp()}$ cm et $OB${sp()}=${sp()}${texNombre(c2, 1)}${sp()}$ cm.<br>`
        texte += ` Le point O' est situé sur la hauteur [SO] à ${texNombre(h2, 0)}${sp()}cm de S.`
        texte += '<br>Un plan parallèle à la face OAB passant par O\' coupe la pyramide en formant la section O\'A\'B\'.<br>'
        if (!context.isHtml) { texte += 'La figure n\'est pas en vraie grandeur.<br>' }
        texte += numAlpha(0) + ' Calculer l\'' + katexPopup2(numeroExercice, 1, 'aire de base de la pyramide', 'Formule : Aire d\'un triangle rectangle', '$Aire=\\dfrac{\\text{c}\\times\\text{c\'}}{2}$') + '.<br>'
        texte += numAlpha(1) + ' Calculer le ' + katexPopup2(numeroExercice + 5, 1, 'volume de la pyramide', 'Formule : volume d\'une pyramide d\'aire de base $B$ et de hauteur h', '$Volume= \\dfrac{B \\times \\text{h}}{3}$') + ' SOAB.<br>'
        texte += numAlpha(2) + ' En déduire l\'aire de la ' + katexPopup2(numeroExercice + 10, 1, 'section', 'Définition : section plane d\'un solide', `La section d'un solide par un plan est une figure plane.<br>Dans le cas d'une section d'une pyramide par un plan parallèle à sa base, cette section est un polygone qui est une réduction de la base.<br>Dans une réduction de coefficient k, les aires sont multipliées par k${texteExposant(2)} et les volumes sont multipliés par k${texteExposant(3)}.`) + ` O'A'B' sachant que SO'${sp()}=${sp()}${texNombre(h2, 0)}${sp()}cm.<br>`
        texte += numAlpha(3) + ' Calculer le volume de la pyramide SO\'A\'B\'.<br>'
        texte += numAlpha(4) + ' Calculer le volume du tronc de la pyramide (partie de la pyramide située entre la base et la section).'
        if (context.isHtml) { texte += '<br>Le point O peut être déplacé et on peut changer l\'angle de vue &#x3C6; ' } else {
          texte += `\n\t \\end{minipage} \n\t \\begin{minipage}{0.3 \\linewidth} \n\t \\begin{tikzpicture}[scale=0.8]
          \\definecolor{hhhhhh}{rgb}{0,0,0}
          \\definecolor{phphph}{rgb}{0.5,0.5,0.5}
          \\definecolor{ofofof}{rgb}{0.5,0.5,0.5}
          \\definecolor{ffhhhh}{rgb}{1,0,0}
          \\definecolor{hhofhh}{rgb}{0,0.5,0}
          \\definecolor{hhhhff}{rgb}{0,0,1}
          \\clip (8.05,0) rectangle (0,12.08);
          \\fill[color=black] (3.878,2.24) circle (0.054);
          \\node at (3.341, 2.562) [align=left,inner sep = 0pt, outer sep = 0pt,below right,black,font= \\sf \\fontsize {0.376cm} {0.47cm} \\selectfont] {$\\text{O}$};
          \\fill[color=black] (3.878,7.567) circle (0.054);
          \\node at (3.663, 7.889) [align=left,inner sep = 0pt, outer sep = 0pt,below right,black,font= \\sf \\fontsize {0.376cm} {0.47cm} \\selectfont] {$\\text{O'}$};
          \\draw [color=black , dotted, line width = 0.4](1.822,1.235)--(3.878,2.24);
          \\draw [color=black , dotted, line width = 0.4](3.878,2.24)--(6.791,0.978);
          \\draw [color=black , dotted, line width = 0.4](6.791,0.978)--(1.822,1.235);
          \\draw [color=black , dotted, line width = 0.4](3.878,11.118)--(1.822,1.235);
          \\draw [color=black , dotted, line width = 0.4](3.878,11.118)--(6.791,0.978);
          \\draw [color=black , dotted, line width = 0.4](3.055,7.165)--(3.878,7.567);
          \\draw [color=black , dotted, line width = 0.4](3.878,7.567)--(5.043,7.062);
          \\draw [color=black , dotted, line width = 0.4](3.055,7.165)--(5.043,7.062);
          \\draw [color=black , line width = 0.8](3.878,11.118)--(1.822,1.235);
          \\draw [color=black , line width = 0.8](3.878,11.118)--(6.791,0.978);
          \\draw [color=black , dotted, line width = 0.4](3.878,11.118)--(3.878,2.24);
          \\draw [color=black , line width = 0.8](3.055,7.165)--(5.043,7.062);
          \\node at (2.345, 7.43) [align=left,below right ,black,,font= \\sf \\fontsize {0.403cm} {0.503cm} \\selectfont] {\\textbf{A'}};
          \\node at (5.278, 7.27) [align=left,below right ,black,,font= \\sf \\fontsize {0.403cm} {0.503cm} \\selectfont] {\\textbf{B'}};
          \\node at (1.178, 1.584) [align=left,below right ,black,,font= \\sf \\fontsize {0.403cm} {0.503cm} \\selectfont] {\\textbf{A}};
          \\node at (7.155, 1.145) [align=left,below right ,black,,font= \\sf \\fontsize {0.403cm} {0.503cm} \\selectfont] {\\textbf{B}};
          \\draw [color=ofofof , dotted, line width = 0.4](3.878,2.24)--(4.242,2.083);
          \\draw [color=ofofof , dotted, line width = 0.4](3.535,2.073)--(3.878,2.24);
          \\draw [color=ofofof , dotted, line width = 0.4](3.535,2.073)--(3.899,1.915);
          \\draw [color=ofofof , dotted, line width = 0.4](3.899,1.915)--(4.242,2.083);
          \\draw [color=ofofof , dotted, line width = 0.4](4.242,2.083)--(3.878,2.24)--(3.535,2.073)--(3.899,1.915)--(4.242,2.083)--cycle;
          \\draw [color=ofofof , dotted, line width = 0.4](3.878,7.567)--(4.242,7.409);
          \\draw [color=ofofof , dotted, line width = 0.4](3.535,7.399)--(3.878,7.567);
          \\draw [color=ofofof , dotted, line width = 0.4](3.535,7.399)--(3.899,7.241);
          \\draw [color=ofofof , dotted, line width = 0.4](3.899,7.241)--(4.242,7.409);
          \\draw [color=ofofof , dotted, line width = 0.4](4.242,7.409)--(3.878,7.567)--(3.535,7.399)--(3.899,7.241)--(4.242,7.409)--cycle;
          \\draw [color=ofofof , dotted, line width = 0.4](3.878,2.684)--(3.878,2.24);
          \\draw [color=ofofof , dotted, line width = 0.4](4.242,2.083)--(4.242,2.526);
          \\draw [color=ofofof , dotted, line width = 0.4](4.242,2.526)--(3.878,2.684);
          \\draw [color=ofofof , dotted, line width = 0.4](3.878,2.684)--(3.878,2.24)--(4.242,2.083)--(4.242,2.526)--(3.878,2.684)--cycle;
          \\draw [color=ofofof , dotted, line width = 0.4](3.878,2.684)--(3.535,2.517);
          \\draw [color=ofofof , dotted, line width = 0.4](3.535,2.517)--(3.535,2.073);
          \\draw [color=ofofof , dotted, line width = 0.4](3.535,2.073)--(3.878,2.24)--(3.878,2.684)--(3.535,2.517)--(3.535,2.073)--cycle;
          \\draw [color=ofofof , dotted, line width = 0.4](3.878,8.011)--(3.878,7.567);
          \\draw [color=ofofof , dotted, line width = 0.4](4.242,7.409)--(4.242,7.853);
          \\draw [color=ofofof , dotted, line width = 0.4](4.242,7.853)--(3.878,8.011);
          \\draw [color=ofofof , dotted, line width = 0.4](3.878,8.011)--(3.878,7.567)--(4.242,7.409)--(4.242,7.853)--(3.878,8.011)--cycle;
          \\draw [color=ofofof , dotted, line width = 0.4](3.878,8.011)--(3.535,7.843);
          \\draw [color=ofofof , dotted, line width = 0.4](3.535,7.843)--(3.535,7.399);
          \\draw [color=ofofof , dotted, line width = 0.4](3.535,7.399)--(3.878,7.567)--(3.878,8.011)--(3.535,7.843)--(3.535,7.399)--cycle;
          \\draw [color=ffhhhh , dotted, line width = 0.4](3.055,7.165)--(5.043,7.062)--(3.878,7.567)--(3.055,7.165)--cycle;
          \\fill [color = ffhhhh, opacity = 0.2](3.055,7.165)--(5.043,7.062)--(3.878,7.567)--(3.055,7.165)--cycle;
          \\draw [color=hhofhh , dotted, line width = 0.4](1.822,1.235)--(6.791,0.978)--(3.878,2.24)--(1.822,1.235)--cycle;
          \\fill [color = hhhhff, opacity = 0.2](1.822,1.235)--(6.791,0.978)--(3.878,2.24)--(1.822,1.235)--cycle;
          \\node at (3.395, 11.857) [align=left,below right ,black,,font= \\sf \\fontsize {0.403cm} {0.503cm} \\selectfont] {\\textbf{S}};
          \\end{tikzpicture} \n\t \\end{minipage}`
        }

        texteCorr = numAlpha(0) + ` L'aire de base de la pyramide est : $\\dfrac{${texNombre(c, 1)}\\times${texNombre(c2, 1)}}{2}$ cm${texteExposant(2)} $= ${texNombre(c.mul(c2).div(2), 3)}$ cm${texteExposant(2)}.<br>`
        texteCorr += numAlpha(1) + ` Le volume de la pyramide est : $\\dfrac{A_\\text{base} \\times \\text{hauteur}}{3}$ cm${texteExposant(3)} $= \\dfrac{${texNombre(c.mul(c2).div(2), 3)}\\times ${texNombre(h1, 1)}}{3}$ cm${texteExposant(3)} $\\approx ${texNombre(c.mul(c2).mul(h1).div(6), 3)}$ cm${texteExposant(3)}.<br>`
        texteCorr += numAlpha(2) + ` La section est une réduction de la base de coefficient $${texFractionReduite(h2.mul(10), h1.mul(10))}$.<br>`
        texteCorr += `Dans une réduction de coefficient k, les aires sont multipliés par k${texteExposant(2)}.<br>`
        texteCorr += `Donc son aire est $\\left(${texFractionReduite(h2.mul(10), h1.mul(10))}\\right)^2 \\times ${texNombre(c.mul(c2).div(2), 3)}$ cm${texteExposant(2)} $=${texFractionReduite(h2.mul(h2).mul(100).mul(c).mul(c2), h1.mul(h1).mul(200))}$ cm${texteExposant(2)} $\\approx ${texNombre(h2.div(h1).pow(2).mul(c).mul(c2).div(2), 2)}$ cm${texteExposant(2)}.<br>`
        texteCorr += numAlpha(3) + ` Dans une réduction de coefficient k, les volumes sont multipliés par k${texteExposant(3)}.<br>`
        texteCorr += `Donc le volume de la pyramide SO'A'B' est : $\\left(${texFractionReduite(h2.mul(10), h1.mul(10))}\\right)^3 \\times \\dfrac{${texNombre(c.mul(c2).mul(h1).div(2), 3)}}{3}$ cm${texteExposant(3)} $\\approx ${texNombre(h2.pow(3).mul(c).mul(c2).div(h1.pow(2)).div(6), 2)}$ cm${texteExposant(3)} '.<br>`
        texteCorr += numAlpha(4) + ' Le volume du tronc de la pyramide est : '
        texteCorr += `$V_\\text{SABCD} - V_\\text{SA'B'C'D'}$<br>Soit : <br>$${texNombre(c.mul(c2).mul(h1).div(6), 3)}$ cm${texteExposant(3)}$ - ${texNombre(h2.pow(3).mul(c).mul(c2).div(h1.pow(2)).div(6), 3)}$ cm${texteExposant(3)}$ \\approx ${texNombre(c.mul(c2).mul(h1).div(6).sub(h2.pow(3).mul(c).mul(c2).div(h1.pow(2)).div(6)), 2)}$ cm${texteExposant(3)}.<br>`
        texteCorr += `Ce qui représente $${texFractionReduite(h1.pow(3).sub(h2.pow(3)).mul(1000), h1.pow(3).mul(1000))}$ du volume de SABCD.`

        this.MG32codeBase64 = codeBase64
        this.mg32init = (mtg32App, idDoc) => {
          mtg32App.giveFormula2(idDoc, 'c', c.toString())
          mtg32App.giveFormula2(idDoc, 'h1', h1.toString())
          mtg32App.giveFormula2(idDoc, 'h2', texNombre(h2, 0))
          mtg32App.giveFormula2(idDoc, "c'", c2.toString())
          mtg32App.calculate(idDoc, true)
          return mtg32App.display(idDoc)
        }
        break
      case 4: // Un tronc de cône étant donné (seau), calcul de la hauteur du cône dont il est issu, de son volume, puis du volume du seau. Lecture graphique du volume d'eau à mi hauteur et calcul de ce volume

        r = new Decimal(randint(15, 20)).div(10)
        r2 = new Decimal(randint(11, r * 10 - 3)).div(10)
        h3 = new Decimal(randint(10, 15)).div(5)
        h2 = r2.mul(h3).div(r.sub(r2))
        h1 = h2.plus(h3)
        while (!h2.div(h1).mul(10).eq(h2.div(h1).mul(10).round()) || !h3.div(2).plus(h2).div(h1).mul(10).eq(h3.div(2).plus(h2).div(h1).mul(10).round())) { // on impose des coefficients de réduction décimaux dans cet exercice.
          r = new Decimal(randint(15, 20)).div(10)
          r2 = new Decimal(randint(11, r * 10 - 3)).div(10)
          h3 = new Decimal(randint(10, 15)).div(5)
          h2 = r2.mul(h3).div(r.sub(r2))
          h1 = h2.plus(h3)
        }
        codeBase64 = 'TWF0aEdyYXBoSmF2YTEuMAAAABI+qPXDAANmcmH###8BAP8BAAAAAAAAAAAFHAAAAtIAAAAAAAAAAAAAAAEAAAE8#####wAAAAEACkNDYWxjQ29uc3QA#####wACcGkAFjMuMTQxNTkyNjUzNTg5NzkzMjM4NDb#####AAAAAQAKQ0NvbnN0YW50ZUAJIftURC0Y#####wAAAAEACkNQb2ludEJhc2UA#####wEAAAAAEAAAAEAIAAAAAAAAAAAAAAAAAAAFAABAIwAAAAAAAEB7iFHrhR64#####wAAAAEAB0NDYWxjdWwA#####wAFbWluaTMAAzAuMgAAAAE#yZmZmZmZmgAAAAMA#####wAFbWF4aTMAATIAAAABQAAAAAAAAAD#####AAAAAQAUQ0ltcGxlbWVudGF0aW9uUHJvdG8A#####wAHQ3Vyc2V1cgAAAAUAAAAFAAAAAwAAAAIAAAADAAAAAf####8AAAABABRDRHJvaXRlRGlyZWN0aW9uRml4ZQAAAAAEAQAAAAAQAAABAAEAAAABAT#wAAAAAAAA#####wAAAAEAD0NQb2ludExpZURyb2l0ZQEAAAAEAQAAAAAQAAAAwAgAAAAAAAA#8AAAAAAAAAUAAUBLgAAAAAAAAAAABf####8AAAABAAtDSG9tb3RoZXRpZQAAAAAEAAAAAf####8AAAABAApDT3BlcmF0aW9uA#####8AAAABAA9DUmVzdWx0YXRWYWxldXIAAAACAAAACAEAAAAJAAAAAgAAAAkAAAAD#####wAAAAEAC0NQb2ludEltYWdlAAAAAAQBAAAAAA0AAk8xAMAQAAAAAAAAQBAAAAAAAAAFAAAAAAYAAAAHAAAABwAAAAAEAAAAAQAAAAgDAAAACAEAAAABP#AAAAAAAAAAAAAJAAAAAgAAAAgBAAAACQAAAAMAAAAJAAAAAgAAAAoAAAAABAEAAAAADQACSTEAwAAAAAAAAABACAAAAAAAAAUAAAAABgAAAAn#####AAAAAQAIQ1NlZ21lbnQBAAAABAAAAAAAEAAAAQEBAAAAAQAAAAYAAAAGAQAAAAQAAAAAARAAAmsxAMAAAAAAAAAAQAAAAAAAAAABAAE#0p5BKeQSngAAAAv#####AAAAAgAPQ01lc3VyZUFic2Npc3NlAQAAAAQABHpvb20AAAAIAAAACgAAAAz#####AAAAAQAPQ1ZhbGV1ckFmZmljaGVlAQAAAAQBAAAAAAAAAAAAAAAAwBgAAAAAAAAAAAAMDwAB####AAAAAQAAAAIAAAABAAAAAAAAAAAAAAAAAgAAAA0AAAADAP####8ABVJtaW5pAAIxNQAAAAFALgAAAAAAAAAAAAMA#####wAFUm1heGkAAjIwAAAAAUA0AAAAAAAAAAAAAwD#####AAZSbWF4aScAB1JtYXhpLTUAAAAIAQAAAAkAAAAQAAAAAUAUAAAAAAAAAAAAAwD#####AAVIbWF4aQACMzAAAAABQD4AAAAAAAAAAAADAP####8ABUhtaW5pAAIyMAAAAAFANAAAAAAAAAAAAAIA#####wAAAAAAEAAAAEAIAAAAAAAAAAAAAAAAAAAFAABAbJAAAAAAAECANCj1wo9cAAAAAwD#####AARwYXM0AAExAAAAAT#wAAAAAAAAAAAAAwD#####AAhwYXNncmFkNAABNQAAAAFAFAAAAAAAAAAAAAQA#####wAHQ3Vyc2V1cgAAAA4AAAAHAAAABQAAABMAAAASAAAAFQAAABYAAAAUAAAABQAAAAAXAQAAAAAQAAABAAEAAAAUAT#wAAAAAAAAAAAABgEAAAAXAAAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAEBhgAAAAAAAAAAAGAAAAAMAAAAAFwAHbmJncmFkMAAdaW50KChIbWF4aS1IbWluaSkvcGFzNCswLjUpKzEAAAAIAP####8AAAACAAlDRm9uY3Rpb24CAAAACAAAAAAIAwAAAAgBAAAACQAAABIAAAAJAAAAEwAAAAkAAAAVAAAAAT#gAAAAAAAAAAAAAT#wAAAAAAAAAAAAAwAAAAAXAApuYmdyYWRwYXMwACFpbnQoKEhtYXhpLUhtaW5pKS9wYXNncmFkNCswLjUpKzEAAAAIAAAAAA4CAAAACAAAAAAIAwAAAAgBAAAACQAAABIAAAAJAAAAEwAAAAkAAAAWAAAAAT#gAAAAAAAAAAAAAT#wAAAAAAAA#####wAAAAEAC0NQb2ludENsb25lAAAAABcBAAAAAAsAAk8xAMA4AAAAAAAAP#AAAAAAAAABAAAAABQAAAALAQAAABcAAAAAABAAAAEAAQAAABwAAAAZ#####wAAAAEAFkNEcm9pdGVQZXJwZW5kaWN1bGFpcmUAAAAAFwEAAAAAEAAAAQABAAAAHAAAAB0AAAAGAAAAABcBAAAAAAsAAkoxAMA2AAAAAAAAwC4AAAAAAAABAAG#vhkUx7D9WQAAAB4AAAAHAAAAABcAAAAcAAAACAMAAAAJAAAAFQAAAAgBAAAACQAAABIAAAAJAAAAEwAAAAoAAAAAFwEAAAAACwACSTEAAAAAAAAAAABAAAAAAAAAAAEAAAAAGQAAACD#####AAAAAgAHQ1JlcGVyZQAAAAAXAAAAAAEBAAAAHAAAACEAAAAfAAAAAAAACQAAABMAAAABAAAAAAAAAAAAAAAJAAAAFQAAAAE#8AAAAAAAAAAAAAYAAAAAFwEAAAAACwACVzEAwCAAAAAAAADAOwAAAAAAAAUAAT#hGDFObkU6AAAAHf####8AAAACABJDTGlldU9iamV0UGFyUHRMaWUBAAAAFwAAAAAAAAAjAAAACQAAABoAAAAjAAAAAgAAACMAAAAj#####wAAAAIACENNZXN1cmVYAAAAABcABGFic3cAAAAiAAAAIwAAAAMAAAAAFwAHYWJzd0FycgAjaW50KGFic3cqMTAwMDAwMDAwMCswLjUpLzEwMDAwMDAwMDAAAAAIAwAAAA4CAAAACAAAAAAIAgAAAAkAAAAlAAAAAUHNzWUAAAAAAAAAAT#gAAAAAAAAAAAAAUHNzWUAAAAAAAAADQAAAAAXAQAAAAAAAAAAAAAAAEAYAAAAAAAAAAAAIwsAAAAAAAEAAAAAAAAAAQAAAAAAAAAAAAAAAAkAAAAmAAAAEgEAAAAXAAAAAAAAACcAAAAJAAAAGwAAACMAAAAEAAAAIwAAACUAAAAmAAAAJ#####8AAAABAA1DUG9pbnRCYXNlRW50AQAAABcAAAAAARAAAlQzAAAAAAAAAAAAQAgAAAAAAAABAAEAAAAiQCAAAAAAAAAAAAAAAAAAAAAAAAAACQAAABMAAAAJAAAAEgAAAAEAAAAAAAAAAAAAAAEAAAAAAAAAAAAAABMAAAAAFwAFbWVzYWIAAAAiAAAAKQAAAAMBAAAAFwACaDUAJGludChtZXNhYioxMDAwMDAwMDAwKzAuNSkvMTAwMDAwMDAwMAAAAAgDAAAADgIAAAAIAAAAAAgCAAAACQAAACoAAAABQc3NZQAAAAAAAAABP+AAAAAAAAAAAAABQc3NZQAAAAAAAAANAQAAABcAAAAAAAAAAAAAAAAAwCAAAAAAAAAAAAApDwAB####AAAAAQAAAAIAAAABAAAAAAAAAAAABUJIID0gAAMgY20JAAAAKwAAAAMA#####wAGUm1pbmknAAIxMAAAAAFAJAAAAAAAAAAAAAIA#####wAAAAAAEAAAAEAIAAAAAAAAAAAAAAAAAAAFAABAbLAAAAAAAEB9eFHrhR64AAAAAwD#####AARwYXMyAAExAAAAAT#wAAAAAAAAAAAAAwD#####AAhwYXNncmFkMgABNQAAAAFAFAAAAAAAAAAAAAQA#####wAHQ3Vyc2V1cgAAAA4AAAAHAAAABQAAAC0AAAARAAAALwAAADAAAAAuAAAABQAAAAAxAQAAAAAQAAABAAEAAAAuAT#wAAAAAAAAAAAABgEAAAAxAAAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAEBhgAAAAAAAAAAAMgAAAAMAAAAAMQAHbmJncmFkMAAfaW50KChSbWF4aSctUm1pbmknKS9wYXMyKzAuNSkrMQAAAAgAAAAADgIAAAAIAAAAAAgDAAAACAEAAAAJAAAAEQAAAAkAAAAtAAAACQAAAC8AAAABP+AAAAAAAAAAAAABP#AAAAAAAAAAAAADAAAAADEACm5iZ3JhZHBhczAAI2ludCgoUm1heGknLVJtaW5pJykvcGFzZ3JhZDIrMC41KSsxAAAACAAAAAAOAgAAAAgAAAAACAMAAAAIAQAAAAkAAAARAAAACQAAAC0AAAAJAAAAMAAAAAE#4AAAAAAAAAAAAAE#8AAAAAAAAAAAAA8AAAAAMQEAAAAACwACTzEAwDgAAAAAAAA#8AAAAAAAAAEAAAAALgAAAAsBAAAAMQAAAAAAEAAAAQABAAAANgAAADMAAAAQAAAAADEBAAAAABAAAAEAAQAAADYAAAA3AAAABgAAAAAxAQAAAAALAAJKMQDANgAAAAAAAMAuAAAAAAAAAQABv74ZFMew#VkAAAA4AAAABwAAAAAxAAAANgAAAAgDAAAACQAAAC8AAAAIAQAAAAkAAAARAAAACQAAAC0AAAAKAAAAADEBAAAAAAsAAkkxAAAAAAAAAAAAQAAAAAAAAAABAAAAADMAAAA6AAAAEQAAAAAxAAAAAAEBAAAANgAAADsAAAA5AAAAAAAACQAAAC0AAAABAAAAAAAAAAAAAAAJAAAALwAAAAE#8AAAAAAAAAAAAAYAAAAAMQEAAAAACwACVzEAwCAAAAAAAADAOwAAAAAAAAUAAT#hGDFObkU6AAAANwAAABIBAAAAMQAAAAAAAAA9AAAACQAAADQAAAA9AAAAAgAAAD0AAAA9AAAAEwAAAAAxAARhYnN3AAAAPAAAAD0AAAADAAAAADEAB2Fic3dBcnIAI2ludChhYnN3KjEwMDAwMDAwMDArMC41KS8xMDAwMDAwMDAwAAAACAMAAAAOAgAAAAgAAAAACAIAAAAJAAAAPwAAAAFBzc1lAAAAAAAAAAE#4AAAAAAAAAAAAAFBzc1lAAAAAAAAAA0AAAAAMQEAAAAAAAAAAAAAAABAGAAAAAAAAAAAAD0LAAAAAAABAAAAAAAAAAEAAAAAAAAAAAAAAAAJAAAAQAAAABIBAAAAMQAAAAAAAABBAAAACQAAADUAAAA9AAAABAAAAD0AAAA#AAAAQAAAAEEAAAAUAQAAADEAAAAAARAAAVQAAAAAAAAAAABACAAAAAAAAAEAAQAAADxAFAAAAAAAAAAAAAAAAAAAAAAAAAAJAAAALQAAAAkAAAARAAAAAQAAAAAAAAAAAAAAAQAAAAAAAAAAAAAAEwAAAAAxAAVtZXNhYgAAADwAAABDAAAAAwEAAAAxAAJyMwAkaW50KG1lc2FiKjEwMDAwMDAwMDArMC41KS8xMDAwMDAwMDAwAAAACAMAAAAOAgAAAAgAAAAACAIAAAAJAAAARAAAAAFBzc1lAAAAAAAAAAE#4AAAAAAAAAAAAAFBzc1lAAAAAAAAAA0BAAAAMQAAAAAAAAAAAAAAAADAIAAAAAAAAAAAAEMPAAH###8AAAABAAAAAgAAAAEAAAAAAAAAAAAFQkEgPSAAAyBjbQkAAABFAAAAAgD#####AAAAAAAQAAAAQAgAAAAAAAAAAAAAAAAAAAUAAEBs8AAAAAAAQHo4UeuFHrgAAAADAP####8ABW1pbmkxAAVSbWluaQAAAAkAAAAPAAAAAwD#####AAVtYXhpMQAFUm1heGkAAAAJAAAAEAAAAAMA#####wAEcGFzMQABMQAAAAE#8AAAAAAAAAAAAAMA#####wAIcGFzZ3JhZDEAATUAAAABQBQAAAAAAAAAAAAEAP####8AB0N1cnNldXIAAAAOAAAABwAAAAUAAABIAAAASQAAAEoAAABLAAAARwAAAAUAAAAATAEAAAAAEAAAAQABAAAARwE#8AAAAAAAAAAAAAYBAAAATAAAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAABAYYAAAAAAAAAAAE0AAAADAAAAAEwAB25iZ3JhZDAAHWludCgobWF4aTEtbWluaTEpL3BhczErMC41KSsxAAAACAAAAAAOAgAAAAgAAAAACAMAAAAIAQAAAAkAAABJAAAACQAAAEgAAAAJAAAASgAAAAE#4AAAAAAAAAAAAAE#8AAAAAAAAAAAAAMAAAAATAAKbmJncmFkcGFzMAAhaW50KChtYXhpMS1taW5pMSkvcGFzZ3JhZDErMC41KSsxAAAACAAAAAAOAgAAAAgAAAAACAMAAAAIAQAAAAkAAABJAAAACQAAAEgAAAAJAAAASwAAAAE#4AAAAAAAAAAAAAE#8AAAAAAAAAAAAA8AAAAATAEAAAAACwACTzEAwDgAAAAAAAA#8AAAAAAAAAEAAAAARwAAAAsBAAAATAAAAAAAEAAAAQABAAAAUQAAAE4AAAAQAAAAAEwBAAAAABAAAAEAAQAAAFEAAABSAAAABgAAAABMAQAAAAALAAJKMQDANgAAAAAAAMAuAAAAAAAAAQABv74ZFMew#VkAAABTAAAABwAAAABMAAAAUQAAAAgDAAAACQAAAEoAAAAIAQAAAAkAAABJAAAACQAAAEgAAAAKAAAAAEwBAAAAAAsAAkkxAAAAAAAAAAAAQAAAAAAAAAABAAAAAE4AAABVAAAAEQAAAABMAAAAAAEBAAAAUQAAAFYAAABUAAAAAAAACQAAAEgAAAABAAAAAAAAAAAAAAAJAAAASgAAAAE#8AAAAAAAAAAAAAYAAAAATAEAAAAACwACVzEAwCAAAAAAAADAOwAAAAAAAAUAAT#hGDFObkU6AAAAUgAAABIBAAAATAAAAAAAAABYAAAACQAAAE8AAABYAAAAAgAAAFgAAABYAAAAEwAAAABMAARhYnN3AAAAVwAAAFgAAAADAAAAAEwAB2Fic3dBcnIAI2ludChhYnN3KjEwMDAwMDAwMDArMC41KS8xMDAwMDAwMDAwAAAACAMAAAAOAgAAAAgAAAAACAIAAAAJAAAAWgAAAAFBzc1lAAAAAAAAAAE#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####AAAAAQAAAAIAAAABAAAAAAAAAAAABEhMID0AAyBjbQkAAABgAAAAAwD#####AAJoMwAFaDUvMTAAAAAIAwAAAAkAAAArAAAAAUAkAAAAAAAAAAAAAwD#####AAJyJwAFcjMvMTAAAAAIAwAAAAkAAABFAAAAAUAkAAAAAAAAAAAAAwD#####AAFyAAVyMi8xMAAAAAgDAAAACQAAAGAAAAABQCQAAAAAAAAAAAADAP####8AAmgyAAxyJypoMy8oci1yJykAAAAIAwAAAAgCAAAACQAAAGMAAAAJAAAAYgAAAAgBAAAACQAAAGQAAAAJAAAAYwAAAAIA#####wAAAAABDAABUwDALgAAAAAAAMAiAAAAAAAABQABQFugAAAAAABAfOhR64UeuAAAAAcA#####wAAAGYAAAAJAAAAZQAAAAcA#####wAAAGYAAAAJAAAADQAAAAMA#####wAISGVhdU1pbmkAATAAAAABAAAAAAAAAAAAAAACAP####8AAAAAABAAAABACAAAAAAAAAAAAAAAAAAABQAAQGxQAAAAAABAgfwo9cKPXAAAAAMA#####wAEcGFzNQABMQAAAAE#8AAAAAAAAAAAAAQA#####wAHQ3Vyc2V1cgAAAAoAAAAGAAAABAAAAGkAAAArAAAAawAAAGoAAAAFAAAAAGwBAAAAABAAAAEAAQAAAGoBP#AAAAAAAAAAAAAGAQAAAGwAAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAQGGAAAAAAAAAAABtAAAAAwAAAABsAAduYmdyYWQwAB1pbnQoKGg1LUhlYXVNaW5pKS9wYXM1KzAuNSkrMQAAAAgAAAAADgIAAAAIAAAAAAgDAAAACAEAAAAJAAAAKwAAAAkAAABpAAAACQAAAGsAAAABP+AAAAAAAAAAAAABP#AAAAAAAAAAAAAPAAAAAGwBAAAAAAsAAk8xAMA4AAAAAAAAP#AAAAAAAAABAAAAAGoAAAALAQAAAGwAAAAAABAAAAEAAQAAAHAAAABuAAAAEAAAAABsAQAAAAAQAAABAAEAAABwAAAAcQAAAAYAAAAAbAEAAAAACwACSjEAwDYAAAAAAADALgAAAAAAAAEAAb++GRTHsP1ZAAAAcgAAAAcAAAAAbAAAAHAAAAAIAwAAAAkAAABrAAAACAEAAAAJAAAAKwAAAAkAAABpAAAACgAAAABsAQAAAAALAAJJMQAAAAAAAAAAAEAAAAAAAAAAAQAAAABuAAAAdAAAABEAAAAAbAAAAAABAQAAAHAAAAB1AAAAcwAAAAAAAAkAAABpAAAAAQAAAAAAAAAAAAAACQAAAGsAAAABP#AAAAAAAAAAAAAGAAAAAGwBAAAAAAsAAlcxAMAgAAAAAAAAwDsAAAAAAAAFAAE#4RgxTm5FOgAAAHEAAAASAQAAAGwAAAAAAAAAdwAAAAkAAABvAAAAdwAAAAIAAAB3AAAAdwAAABQBAAAAbAAAAAABEAACVDIAAAAAAAAAAABACAAAAAAAAAEAAQAAAHZAIAAAAAAAAAAAAAAAAAAAAAAAAAAJAAAAaQAAAAkAAAArAAAAAQAAAAAAAAAAAAAAAQAAAAAAAAAAAAAAEwAAAABsAAVtZXNhYgAAAHYAAAB5AAAAAwEAAABsAAJoZQAkaW50KG1lc2FiKjEwMDAwMDAwMDArMC41KS8xMDAwMDAwMDAwAAAACAMAAAAOAgAAAAgAAAAACAIAAAAJAAAAegAAAAFBzc1lAAAAAAAAAAE#4AAAAAAAAAAAAAFBzc1lAAAAAAAAAA0BAAAAbAAAAAAAAAAAAAAAAADAIAAAAAAAAAAAAHkPAAH###8AAAABAAAAAgAAAAEAAAAAAAAAAAARIEhhdXRldXIgZCdlYXUgPSAAAyBjbQkAAAB7AAAAAwD#####AAhIZWF1TWF4aQACaDUAAAAJAAAAKwAAAAMA#####wAFbWluaTIAC0hlYXVNaW5pKjEwAAAACAIAAAAJAAAAaQAAAAFAJAAAAAAAAAAAAAMA#####wAFbWF4aTIACEhlYXVNYXhpAAAACQAAAH0AAAADAP####8ABHBhczMAATEAAAABP#AAAAAAAAAAAAADAP####8ACHBhc2dyYWQzAAE1AAAAAUAUAAAAAAAAAAAAAwD#####AAJoMQAFaDIraDMAAAAIAAAAAAkAAABlAAAACQAAAGL#####AAAAAgAMQ0NvbW1lbnRhaXJlAP####8AAAAAAMAxAAAAAAAAwCgAAAAAAAAAAABmEAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAyNHUwAAAAMA#####wAEaGVhdQAFaGUvMTAAAAAIAwAAAAkAAAB7AAAAAUAkAAAAAAAAAAAABQD#####AQAAAAAQAAABAQEAAABmAD#qqqqqqqqrAAAABgD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAcBGMzMzMzMpAAAAhQAAAAoA#####wEAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAAIYAAABo#####wAAAAEADkNQb2ludExpZVBvaW50AP####8B#wAAAQwAAkknAQUAAAAAhwAAAAoA#####wEAAAABCgABQgEFAAAAAIgAAABnAAAACwD#####AAAAAAAQAAABAQEAAABmAAAAif####8AAAABABFDUG9pbnRQYXJBYnNjaXNzZQD#####AQAAAAAQAAJFMQAAAAAAAAAAAEAIAAAAAAAABQAAAABmAAAAiAAAAAgAAAAACQAAAGUAAAAJAAAAhP####8AAAABAAVDRm9uYwD#####AAFmACFwaS8zKigoeCtoMileMyoocicvaDIpXjItcideMipoMikAAAAIAgAAAAgDAAAACQAAAAAAAAABQAgAAAAAAAAAAAAIAQAAAAgC#####wAAAAEACkNQdWlzc2FuY2UAAAAIAP####8AAAACABFDVmFyaWFibGVGb3JtZWxsZQAAAAAAAAAJAAAAZQAAAAFACAAAAAAAAAAAABkAAAAIAwAAAAkAAABjAAAACQAAAGUAAAABQAAAAAAAAAAAAAAIAgAAABkAAAAJAAAAYwAAAAFAAAAAAAAAAAAAAAkAAABlAAF4AAAABwD#####AAAAZgAAAAkAAACCAAAACgD#####AQAAAAEKAAFIAQUAAAAAiAAAAI0AAAALAP####8AAAAAABAAAAEBAQAAAIkAAACOAAAAFgD#####AAAAAAEKAAFFAQUAAAAAiwAAAAwA#####wAEYWJzMQAAAIkAAACOAAAAkAAAAAMA#####wABeAAMYWJzMSooaDEtaDIpAAAACAIAAAAJAAAAkQAAAAgBAAAACQAAAIIAAAAJAAAAZQAAAAMA#####wABeQAEZih4Kf####8AAAABAA5DQXBwZWxGb25jdGlvbgAAAIwAAAAJAAAAkgAAAAIA#####wAAAAABDAABTwDAKAAAAAAAAEAQAAAAAAAABQABQGsAAAAAAABAdwAAAAAAAAAAAAUA#####wEAAAAAEAAAAQABAAAAlAE#6qqqqqqqqwAAAAYA#####wAAAAABDAABSQDAEAAAAAAAAEAQAAAAAAAABQABQFImZmZmZmYAAACV#####wAAAAEACUNEcm9pdGVBQgD#####AQAAAAAMAAABAAEAAACUAAAAlgAAABAA#####wEAAAABEAAAAQABAAAAlAAAAJUAAAAGAP####8AAAAAAQwAAUoAwCYAAAAAAAAAAAAAAAAAAAUAAcAt87ZFocrzAAAAmAAAABwA#####wEAAAAADAAAAQABAAAAlAAAAJkAAAARAP####8AgICAAQEAAACUAAAAlgAAAJkAAAAAAAABAAAAAAAAAAAAAAABAAAAAAAAAAAAAAABP+AAAAAAAAAAAAABP#AAAAAAAAAAAAADAP####8AB25iZ3JhZHgAATYAAAABQBgAAAAAAAAAAAADAP####8AB25iZ3JhZHkAAjMwAAAAAUA+AAAAAAAA#####wAAAAEAE0NBYnNjaXNzZU9yaWdpbmVSZXAA#####wAFYWJzb3IAAACb#####wAAAAEAE0NPcmRvbm5lZU9yaWdpbmVSZXAA#####wAFb3Jkb3IAAACb#####wAAAAEACkNVbml0ZXhSZXAA#####wAGdW5pdGV4AAAAm#####8AAAABAApDVW5pdGV5UmVwAP####8ABnVuaXRleQAAAJv#####AAAAAQAQQ1BvaW50RGFuc1JlcGVyZQD#####AAAAAAAQAAABBQAAAACbAAAACQAAAJ4AAAAJAAAAnwAAACEA#####wAAAAAAEAAAAQUAAAAAmwAAAAgAAAAACQAAAJ4AAAAJAAAAoAAAAAkAAACfAAAAIQD#####AAAAAAAQAAABBQAAAACbAAAACQAAAJ4AAAAIAAAAAAkAAACfAAAACQAAAKEAAAAHAP####8AAACiAAAACQAAAJwAAAAKAP####8AAAAAABAAAAEFAAAAAKMAAAClAAAABwD#####AAAAogAAAAkAAACdAAAACgD#####AAAAAAAQAAABBQAAAACkAAAApwAAAAsA#####wEAAAAAEAAAAQABAAAAowAAAKYAAAALAP####8BAAAAABAAAAEAAQAAAKQAAACoAAAABgD#####AAAAAAAKAAFXAMAUAAAAAAAAwDQAAAAAAAAFAAE#3EE7izAqegAAAKkAAAATAP####8ABnhDb29yZAAAAJsAAACrAAAAAwD#####AAVhYnN3MQAGeENvb3JkAAAACQAAAKwAAAASAP####8AZmZmAAAAqwAAAAkAAACcAAAAqwAAAAIAAACrAAAAqwAAAAMA#####wAFYWJzdzIADTIqYWJzb3ItYWJzdzEAAAAIAQAAAAgCAAAAAUAAAAAAAAAAAAAACQAAAJ4AAAAJAAAArQAAACEA#####wEAAAAAEAAAAQUAAAAAmwAAAAkAAACvAAAACQAAAJ######AAAAAgAGQ0xhdGV4AP####8BAAAAAAAAAAAAAAAAQBgAAAAAAAAAAACwCgAB####AAAAAQAAAAAAAAABAAAAAAAAAAAAC1xWYWx7YWJzdzJ9AAAABgD#####AQAAAAAKAAFSAEAgAAAAAAAAwCAAAAAAAAAFAAE#0RtOgbToHwAAAKr#####AAAAAgAIQ01lc3VyZVkA#####wAGeUNvb3JkAAAAmwAAALIAAAADAP####8ABW9yZHIxAAZ5Q29vcmQAAAAJAAAAswAAABIA#####wBmZmYAAACyAAAACQAAAJ0AAACyAAAAAgAAALIAAACyAAAAAwD#####AAVvcmRyMgANMipvcmRvci1vcmRyMQAAAAgBAAAACAIAAAABQAAAAAAAAAAAAAAJAAAAnwAAAAkAAAC0AAAAIQD#####AQAAAAAQAAABBQAAAACbAAAACQAAAJ4AAAAJAAAAtgAAACIA#####wFmZmYAwBwAAAAAAAC#8AAAAAAAAAAAALcKAAH###8AAAACAAAAAQAAAAEAAAAAAAAAAAALXFZhbHtvcmRyMn0AAAAhAP####8BAAAAABAAAAEFAAAAAJsAAAABAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAhAP####8AAAAAABAAAAEFAAAAAJsAAAAIAQAAAAkAAACCAAAACQAAAGUAAAABAAAAAAAAAAAAAAALAP####8BAAAAABAAAAEAAQAAALkAAAC6AAAABgD#####AQAAAAAMAAJ4MQEFAAE#4499lAf4#gAAALsAAAATAP####8AB3hDb29yZDEAAACbAAAAvAAAAAMA#####wACeDEAB3hDb29yZDEAAAAJAAAAvQAAAAMA#####wACeTEABWYoeDEpAAAAGwAAAIwAAAAJAAAAvgAAACEA#####wEAAAAAEAAAAQUAAAAAmwAAAAkAAAC+AAAACQAAAL######AAAAAgANQ0xpZXVEZVBvaW50cwD#####AAAA#wACAAAAwAAAAfQAAQAAALwAAAAFAAAAvAAAAL0AAAC+AAAAvwAAAMD#####AAAAAQANQ0RlbWlEcm9pdGVPQQD#####AAAAAAANAAABAAEAAACUAAAAlgAAACEA#####wAAAAAAEAAAAQUAAAAAmwAAAAFACAAAAAAAAAAAAAEAAAAAAAAAAAAAABUA#####wAAAAAAwDYAAAAAAABAOwAAAAAAAAAAAMMOAAH###8AAAACAAAAAAAAAAEAAAAAAAAAAAASTml2ZWF1IGQnZWF1IGVuIGRtAAAAIQD#####AAAAAAAQAAABBQAAAACbAAAAAQAAAAAAAAAAAAAAAUAsAAAAAAAAAAAAJQD#####AAAAAAANAAABAAEAAACUAAAAmQAAAAMA#####wAEeG1pbgABMAAAAAEAAAAAAAAAAAAAAAMA#####wAEeG1heAABMwAAAAFACAAAAAAAAAAAAAMA#####wAEeW1pbgABMAAAAAEAAAAAAAAAAAAAAAMA#####wAEeW1heAACMzAAAAABQD4AAAAAAAAAAAAhAP####8AAAAAABAAAAAAAAAAAAAAAD#jMzMzMzMzAgAAAACbAAAAAQAAAAAAAAAAAAAAAQAAAAAAAAAAAAAAAwD#####AAJkeAALeG1heC14bWluKzEAAAAIAAAAAAgBAAAACQAAAMgAAAAJAAAAxwAAAAE#8AAAAAAAAAAAAAMA#####wACZHkAC3ltYXgteW1pbisxAAAACAAAAAAIAQAAAAkAAADKAAAACQAAAMkAAAABP#AAAAAAAAAAAAAhAP####8AAAAAABAAAAAAAAAAAAAAAD#jMzMzMzMzAgAAAACbAAAACQAAAMcAAAABAAAAAAAAAAAAAAAhAP####8AAAAAABAAAAAAAAAAAAAAAD#jMzMzMzMzAgAAAACbAAAACQAAAMgAAAABAAAAAAAAAAAAAAAhAP####8AAAAAABAAAAAAAAAAAAAAAD#jMzMzMzMzAgAAAACbAAAAAQAAAAAAAAAAAAAACQAAAMkAAAAhAP####8AAAAAABAAAAAAAAAAAAAAAD#jMzMzMzMzAgAAAACbAAAAAQAAAAAAAAAAAAAACQAAAMoAAAALAP####8AAAAAABAAAAEAAQAAAM4AAADPAAAABgD#####AAAAAAAQAAAAAAAAAAAAAAA#4zMzMzMzMwIAAT#Ifmt08DKRAAAA0v####8AAAABAAxDVHJhbnNsYXRpb24A#####wAAAMsAAADQAAAACgD#####AQAAAAAQAAAAAAAAAAAAAAA#4zMzMzMzMwIAAAAA0wAAANQAAAAmAP####8AAADQAAAA0QAAAAoA#####wEAAAAAEAAAAAAAAAAAAAAAP+MzMzMzMzMCAAAAANUAAADWAAAACwD#####AX9#fwAQAAABAQEAAADVAAAA1wAAABIA#####wB#f38AAADYAAAACQAAAMwAAADTAAAABAAAANMAAADVAAAA1wAAANgAAAALAP####8AAAAAABAAAAEAAQAAANEAAADQAAAABgD#####AAAAAAAQAAAAAAAAAAAAAAA#4zMzMzMzMwIAAT#AzbwzbwzcAAAA2gAAACYA#####wAAAMsAAADOAAAACgD#####AAAAAAAQAAAAAAAAAAAAAAA#4zMzMzMzMwIAAAAA2wAAANwAAAAmAP####8AAADOAAAAzwAAAAoA#####wEAAAAAEAAAAAAAAAAAAAAAP+MzMzMzMzMCAAAAAN0AAADeAAAACwD#####AX9#fwAQAAABAQEAAADdAAAA3wAAABIA#####wB#f38AAADgAAAACQAAAM0AAADbAAAABAAAANsAAADdAAAA3wAAAOAAAAAhAP####8BAAAAABAAAAEFAAAAAJsAAAABP+AAAAAAAAAAAAABQD4AAAAAAAD#####AAAAAQAUQ1RyYW5zbGF0aW9uUGFyQ29vcmQA#####wAAAJsAAAABP#AAAAAAAAAAAAABAAAAAAAAAAAAAAAKAP####8BAAAAABAAAAEFAAAAAOIAAADjAAAACgD#####AQAAAAAQAAABBQAAAADkAAAA4wAAAAsA#####wB#f38AEAAAAQEBAAAAlgAAAOIAAAAKAP####8Af39#ABAAAAEFAAAAAJYAAADjAAAACgD#####AH9#fwAQAAABBQAAAADnAAAA4wAAAAsA#####wB#f38AEAAAAQEBAAAA5wAAAOQAAAALAP####8Af39#ABAAAAEBAQAAAOgAAADlAAAAFQD#####AAAAAABAKgAAAAAAAMAAAAAAAAAAAAAAxQ4AAf###wAAAAAAAAACAAAAAQAAAAAAAAAAABFWb2x1bWUgZCdlYXUgZW4gTAAAAAUA#####wEAAAAAEAAAAQEBAAAAiQE#6qqqqqqqq#####8AAAABAAlDTG9uZ3VldXIA#####wAAAGYAAACI#####wAAAAIACUNDZXJjbGVPUgD#####AQAAAAEBAAAAiQAAAAgDAAAACAIAAAAJAAAAZAAAAAkAAABlAAAACQAAAIIA#####wAAAAEAEENJbnREcm9pdGVDZXJjbGUA#####wAAAOwAAADu#####wAAAAEAEENQb2ludExpZUJpcG9pbnQA#####wEAAAAAEAAAAQUAAQAAAO8AAAArAP####8BAAAAABAAAAEFAAIAAADvAAAAAwD#####AAFrAAMxLzQAAAAIAwAAAAE#8AAAAAAAAAAAAAFAEAAAAAAAAP####8AAAABABJDQXJjRGVDZXJjbGVEaXJlY3QA#####wEAAAABAQAAAIkAAADwAAAA8f####8AAAABAA9DUG9pbnRMaWVDZXJjbGUA#####wEAAAAAEAAAAQUAAT#LQPMykWXjAAAA8#####8AAAABAA1DUG9pbnRQcm9qZXRlAP####8BAAAAABAAAAEFAAAAAPQAAADsAAAABwD#####AAAA9QAAAAkAAADyAAAACgD#####AQAAAAAQAAABBQAAAAD0AAAA9gAAACQA#####wAAAAABAQAAAPcAAAAyAAAAAAD0AAAABAAAAPQAAAD1AAAA9gAAAPf#####AAAAAQAPQ1N5bWV0cmllQXhpYWxlAP####8AAADsAAAACgD#####AQAAAAAQAAABBQAAAAD3AAAA+QAAACQA#####wAAAAAAAQAAAPoAAAA8AAAAAAD0AAAABQAAAPQAAAD1AAAA9gAAAPcAAAD6AAAABwD#####AAAAZgAAAAgDAAAACQAAAIIAAAAJAAAAZQAAAAoA#####wEAAAAAEAAAAQUAAAAA8AAAAPwAAAAKAP####8BAAAAABAAAAEFAAAAAPEAAAD8#####wAAAAEACUNDZXJjbGVPQQD#####AQAAAAEBAAAAjgAAAP0AAAAtAP####8BAAAAABAAAAEFAAE#5ntWGuQ8wgAAAP8AAAAFAP####8BAAAAABAAAAEBAQAAAI4BP+qqqqqqqqsAAAAuAP####8BAAAAABAAAAEFAAAAAQAAAAEBAAAABwD#####AAABAgAAAAkAAADyAAAACgD#####AQAAAAAQAAABBQAAAAEAAAABAwAAACQA#####wAAAAAAAQAAAQQAAAB4AAAAAAEAAAAABAAAAQAAAAECAAABAwAAAQQAAAALAP####8AAAAAABAAAAEAAQAAAPEAAAD+AAAACwD#####AAAAAAAQAAABAAEAAADwAAAA#QAAABUA#####wAAAAAAwBgAAAAAAADAAAAAAAAAAAAAAI4MAAAAAAACAAAAAQAAAAEAAAAAAAAAAAADI0dIAAAAFQD#####AAAAAABAFAAAAAAAAMAAAAAAAAAAAAAA#QwAAf###wAAAAAAAAABAAAAAQAAAAAAAAAAAAMjR0wAAAALAP####8AAAAAABAAAAEAAQAAAI4AAAD9AAAACwD#####AAAAAAAQAAABAQEAAACJAAAA8AAAABUA#####wAAAAAAwCQAAAAAAABACAAAAAAAAAAAAJAMAAAAAAACAAAAAQAAAAEAAAAAAAAAAAADI0dFAAAABQD#####AQAAAAAQAAABAQEAAACQAT#qqqqqqqqr#####wAAAAEAEENJbnREcm9pdGVEcm9pdGUA#####wEAAAAAEAAAAQUAAAABDQAAAQf#####AAAAAQARQ1N5bWV0cmllQ2VudHJhbGUA#####wAAAJAAAAAKAP####8BAAAAABAAAAEFAAAAAQ4AAAEPAAAALAD#####AQAAAAEBAAAAkAAAAQ4AAAEQAAAALQD#####AQAAAAAQAAABBQABP9E+5jRTgJoAAAERAAAALgD#####AQAAAAAQAAABBQAAAAESAAABDQAAAAcA#####wAAARMAAAAJAAAA8gAAAAoA#####wEAAAAAEAAAAQUAAAABEgAAARQAAAAkAP####8AAAD#AQEAAAEVAAAAPAAAAAABEgAAAAQAAAESAAABEwAAARQAAAEVAAAALwD#####AAABDQAAAAoA#####wEAAP8AEAAAAQUAAAABFQAAARcAAAAkAP####8AAAD#AAEAAAEYAAAAPAAAAAABEgAAAAUAAAESAAABEwAAARQAAAEVAAABGP####8AAAABABFDU3VyZmFjZURldXhMaWV1eAD#####AAB#fwAAAAUAAAD7AAABGQAAADMA#####wAAAP8AAAAFAAABFgAAARkAAAAhAP####8AfwAAABAAAAEFAAAAAJsAAAAJAAAAkgAAAAEAAAAAAAAAAAAAACEA#####wAAAP8ADgABTQDAHAAAAAAAAMA0AAAAAAAABQAAAACbAAAACQAAAJIAAAAJAAAAkwAAACEA#####wAAAP8AEAAAAQUAAAAAmwAAAAEAAAAAAAAAAAAAAAkAAACTAAAAIgD#####AAAA#wDAJgAAAAAAAAAAAAAAAAAAAAABHgwAAf###wAAAAIAAAABAAAAAQAAAAAAAAAAAARWKHgpAAAACwD#####AAAAAAAQAAABAQEAAAEeAAABHQAAAAsA#####wAAAAAAEAAAAQEBAAABHQAAARwAAAALAP####8AAAAAABAAAAEBAQAAAJAAAAEOAAAAFQD#####AQAAAABAIAAAAAAAAD#wAAAAAAAAAAABDg4AAAAAAAAAAAABAAAAAQAAAAAAAAAAAAFGAAAAFQD#####AQAAAAH#####DkAwAAAAAAAAQCgAAAAAAAABAf#MzAAAAAAAAAAAAAAAAQAAAAAAAAAAABNDYXB0dXJlciBsZSBwb2ludCBFAAAACwD#####AAAAAAAQAAABAAEAAABmAAAA8AAAAAsA#####wAAAAAAEAAAAQABAAAAZgAAAPEAAAAiAP####8AAAAAAf####8OQCgAAAAAAABASYAAAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAdFxiZWdpbnthcnJheX17bH0Ke0JBID0gXFZhbHtyJ30gfQpcXCB7eCA9IEJFIFxhcHByb3ggXFZhbHt4fSBcO2RtfQpcXCB7eSA9IFYoeCkgXGFwcHJveCBcVmFse3l9IFw7IGRtXjN9ClxlbmR7YXJyYXl9#####wAAAAEAEENNYWNyb0FwcGFyaXRpb24A#####wAAAP8B#####wxAeYAAAAAAAEAYAAAAAAAAAgHMzP8AAAAAAAAAAAAAAAEAAAAAAAAAAAAGVm9pciBTAAAAAAAEAAAAigAAASUAAAEmAAAAgwD#####AAAAAQARQ01hY3JvRGlzcGFyaXRpb24A#####wAAAP8B#####wxAfiAAAAAAAEAYAAAAAAAAAgHMzP8AAAAAAAAAAAAAAAEAAAAAAAAAAAAIQ2FjaGVyIFMAAAAAAAUAAABmAAAAigAAASUAAAEmAAAAgwAAABUA#####wEAAAAAAAAAAAAAAABAGAAAAAAAAAAAAKsKAAAAAAABAAAAAAAAAAEAAAAAAAAAAAALI1ZhbChhYnN3MSkAAAASAP####8AZmZmAAABKgAAAAkAAACcAAAAqwAAAAQAAACrAAAArAAAAK0AAAEqAAAAFQD#####AWZmZgDAJAAAAAAAAL#wAAAAAAAAAAAAsgoAAAAAAAIAAAABAAAAAQAAAAAAAAAAAAsjVmFsKG9yZHIxKQAAABIA#####wBmZmYAAAEsAAAACQAAAJ0AAACyAAAABAAAALIAAACzAAAAtAAAASwAAAAVAP####8AZmZmAMAQAAAAAAAAP#AAAAAAAAAAAACUCgAAAAAAAgAAAAAAAAABAAAAAAAAAAAAATAAAAAVAP####8B#wAAAMA0AAAAAAAAwCYAAAAAAAAAAACIEAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAyNHVQAAABUA#####wAAAAAAwCwAAAAAAADAIgAAAAAAAAAAAIkQAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAADI0dCAAAAFQD#####AAAAAABACAAAAAAAAMAmAAAAAAAAAAAA8BAAAAAAAAAAAAAAAAAAAQAAAAAAAAAAAAMjR0EAAAAiAP####8AfwAAAAAAAAAAAAAAQBgAAAAAAAAAAAEcEgAB####AAAAAQAAAAAAAAABAAAAAAAAAAAAAXgAAAAVAP####8A#wAAAf####8QQCUAAAAAAABAfDhR64UeuAIAAAAAAAAAAAAAAAABAAAAAAAAAAAABiNHWk9PTQAAAAMA#####wAIdGVzdGNvbmUABHI9cicAAAAICAAAAAkAAABkAAAACQAAAGMAAAACAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQABQFqgAAAAAABAgxwo9cKPXAAAAAcA#####wAAAGYAAAAJAAABNAAAAAoA#####wAAAAABEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAATUAAAE2AAAAAwD#####AAtDb25lVmlzaWJsZQAKMS90ZXN0Y29uZQAAAAgDAAAAAT#wAAAAAAAAAAAACQAAATQAAAAHAP####8AAABmAAAACQAAATgAAAAKAP####8AAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAAE1AAABOQAAABUA#####wAAAAABAAABOhAAAAAAAAAAAAAAAAAAAQAAAAAAAAAAAClJbCBuJ3kgYSBwYXMgZGUgY8O0bmUgZGFucyBjZXMgY29uZGl0aW9ucwAAAO3##########w=='
        if (!context.isHtml) { texte = '\\begin{minipage}{0.7 \\linewidth} \n\t' } else { texte = '' }
        texte += 'Un seau a la forme d\'un tronc de cône.<br>'
        texte += `Sa hauteur intérieure est de $${texNombre(h3, 1)}${sp()}$dm, sa petite base a un diamètre intérieur de $${texNombre(r2 * 2)}${sp()}$dm et sa grande base (l'ouverture) a un diamètre intérieur de $${texNombre(r * 2)}${sp()}$dm.<br>`
        if (!context.isHtml) { texte += 'La figure n\'est pas en vraie grandeur.<br>' }
        texte += numAlpha(0) + ' Calculer la hauteur du cône obtenu en prolongeant les bords du seau.<br>'
        texte += numAlpha(1) + ' En déduire le volume de ce cône.<br>'
        texte += numAlpha(2) + ' En déduire le volume total du seau.<br>'
        if (context.isHtml) { texte += 'Dans ces deux prochaines questions, on considère qu\'on remplit le seau à mi-hauteur d\'eau.<br>' } else { texte += numAlpha(3) + ' On remplit le seau à mi-hauteur d\'eau. Calculer le volume d\'eau correspondant.' }
        if (context.isHtml) {
          texte += numAlpha(3) + ' Par lecture graphique, après avoir correctement paramétré la figure, lire le volume d\'eau correspondant.<br>'
          texte += numAlpha(4) + ' Retrouver ce résultat par le calcul.<br>'
        }
        if (context.isHtml) { texte += '<br>On peut déplacer le cône avec S et modifier les valeurs avec leurs curseurs respectifs.' } else {
          texte += `\n\t \\end{minipage} \n\t \\begin{minipage}{0.3 \\linewidth} \n\t \\begin{tikzpicture}[scale=0.8]
\\definecolor{hhhhhh}{rgb}{0,0,0}
\\definecolor{phphph}{rgb}{0.5,0.5,0.5}
\\definecolor{ffffff}{rgb}{1,1,1}
\\definecolor{hhhhff}{rgb}{0,0,1}
\\definecolor{hhofof}{rgb}{0,0.5,0.5}
\\clip (7.96,0) rectangle (0,12.29);
\\fill[color=black] (3.836,0.278) circle (0.053);
\\node at (3.331, 0.65) [align=left,below right ,black,,font= \\sf \\fontsize {0.398cm} {0.498cm} \\selectfont] {\\textbf{S}};
\\draw [color=black , dotted, line width = 0.4](3.836,0.278)--(3.836,8.678);
\\draw [color=black , dotted, line width = 0.4](3.836,8.678)--(3.836,11.478);
\\fill[color=black] (3.836,9.678) circle (0.053);
\\draw [color=black , dotted, line width = 0.4](5.336,8.678)--(5.333,8.702)--(5.323,8.726)--(5.308,8.75)--(5.287,8.773)--(5.259,8.796)--(5.226,8.819)--(5.187,8.841)--(5.143,8.862)--(5.093,8.883)--(5.038,8.902)--(4.978,8.921)--(4.913,8.939)--(4.844,8.956)--(4.771,8.971)--(4.694,8.986)--(4.613,8.999)--(4.529,9.011)--(4.443,9.021)--(4.354,9.03)--(4.262,9.038)--(4.169,9.044)--(4.075,9.048)--(3.98,9.051)--(3.884,9.053)--(3.788,9.053)--(3.692,9.051)--(3.596,9.048)--(3.502,9.044)--(3.409,9.038)--(3.318,9.03)--(3.228,9.021)--(3.142,9.011)--(3.058,8.999)--(2.977,8.986)--(2.9,8.971)--(2.827,8.956)--(2.758,8.939)--(2.693,8.921)--(2.634,8.902)--(2.579,8.883)--(2.529,8.862)--(2.484,8.841)--(2.445,8.819)--(2.412,8.796)--(2.385,8.773)--(2.363,8.75)--(2.348,8.726)--(2.339,8.702)--(2.336,8.678);

\\draw [color=black , line width = 0.4](5.336,8.678)--(5.334,8.658)--(5.327,8.638)--(5.317,8.619)--(5.302,8.599)--(5.283,8.58)--(5.26,8.56)--(5.233,8.542)--(5.202,8.523)--(5.167,8.505)--(5.128,8.488)--(5.086,8.471)--(5.04,8.455)--(4.99,8.439)--(4.938,8.424)--(4.882,8.41)--(4.823,8.396)--(4.762,8.383)--(4.698,8.371)--(4.631,8.36)--(4.562,8.35)--(4.492,8.341)--(4.419,8.333)--(4.345,8.325)--(4.269,8.319)--(4.192,8.314)--(4.114,8.31)--(4.035,8.307)--(3.955,8.304)--(3.876,8.303)--(3.796,8.303)--(3.716,8.304)--(3.637,8.307)--(3.558,8.31)--(3.48,8.314)--(3.403,8.319)--(3.327,8.325)--(3.252,8.333)--(3.18,8.341)--(3.109,8.35)--(3.04,8.36)--(2.973,8.371)--(2.909,8.383)--(2.848,8.396)--(2.789,8.41)--(2.734,8.424)--(2.681,8.439)--(2.632,8.455)--(2.586,8.471)--(2.543,8.488)--(2.505,8.505)--(2.47,8.523)--(2.439,8.542)--(2.412,8.56)--(2.389,8.58)--(2.37,8.599)--(2.355,8.619)--(2.344,8.638)--(2.338,8.658)--(2.336,8.678);

\\draw [color=black , line width = 0.4](5.836,11.478)--(5.833,11.504)--(5.825,11.53)--(5.811,11.556)--(5.792,11.582)--(5.768,11.608)--(5.738,11.633)--(5.703,11.657)--(5.663,11.682)--(5.618,11.705)--(5.568,11.728)--(5.513,11.751)--(5.454,11.772)--(5.39,11.793)--(5.322,11.813)--(5.25,11.832)--(5.174,11.85)--(5.094,11.867)--(5.011,11.883)--(4.925,11.898)--(4.836,11.911)--(4.744,11.924)--(4.649,11.935)--(4.552,11.945)--(4.454,11.954)--(4.353,11.961)--(4.251,11.967)--(4.149,11.972)--(4.045,11.975)--(3.94,11.978)--(3.836,11.978)--(3.731,11.978)--(3.627,11.975)--(3.523,11.972)--(3.42,11.967)--(3.318,11.961)--(3.218,11.954)--(3.119,11.945)--(3.022,11.935)--(2.928,11.924)--(2.836,11.911)--(2.746,11.898)--(2.66,11.883)--(2.577,11.867)--(2.497,11.85)--(2.421,11.832)--(2.349,11.813)--(2.281,11.793)--(2.218,11.772)--(2.158,11.751)--(2.104,11.728)--(2.054,11.705)--(2.009,11.682)--(1.969,11.657)--(1.934,11.633)--(1.904,11.608)--(1.879,11.582)--(1.86,11.556)--(1.847,11.53)--(1.838,11.504)--(1.836,11.478)--(1.838,11.452)--(1.847,11.426)--(1.86,11.4)--(1.879,11.374)--(1.904,11.349)--(1.934,11.324)--(1.969,11.299)--(2.009,11.275)--(2.054,11.251)--(2.104,11.228)--(2.158,11.206)--(2.218,11.184)--(2.281,11.164)--(2.349,11.144)--(2.421,11.125)--(2.497,11.107)--(2.577,11.09)--(2.66,11.074)--(2.746,11.059)--(2.836,11.045)--(2.928,11.033)--(3.022,11.021)--(3.119,11.011)--(3.218,11.003)--(3.318,10.995)--(3.42,10.989)--(3.523,10.984)--(3.627,10.981)--(3.731,10.979)--(3.836,10.978)--(3.94,10.979)--(4.045,10.981)--(4.149,10.984)--(4.251,10.989)--(4.353,10.995)--(4.454,11.003)--(4.552,11.011)--(4.649,11.021)--(4.744,11.033)--(4.836,11.045)--(4.925,11.059)--(5.011,11.074)--(5.094,11.09)--(5.174,11.107)--(5.25,11.125)--(5.322,11.144)--(5.39,11.164)--(5.454,11.184)--(5.513,11.206)--(5.568,11.228)--(5.618,11.251)--(5.663,11.275)--(5.703,11.299)--(5.738,11.324)--(5.768,11.349)--(5.792,11.374)--(5.811,11.4)--(5.825,11.426)--(5.833,11.452);

\\draw [color=black , line width = 0.4](2.336,8.678)--(1.836,11.478);
\\draw [color=black , line width = 0.4](5.336,8.678)--(5.836,11.478);
\\node at (3.729, 11.531) [align=left,left ,black,,font= \\sf \\fontsize {0.292cm} {0.365cm} \\selectfont] {\\textbf{H}};
\\node at (5.915, 11.531) [align=left,right ,black,fill=ffffff,,font= \\sf \\fontsize {0.292cm} {0.365cm} \\selectfont] {\\textbf{L}};
\\draw [color=black , line width = 0.4](3.836,11.478)--(5.836,11.478);
\\draw [color=black , dotted, line width = 0.4](3.836,8.678)--(5.336,8.678);
\\node at (3.623, 9.599) [align=left,left ,black,,font= \\sf \\fontsize {0.292cm} {0.365cm} \\selectfont] {\\textbf{E}};
\\draw [color=hhhhff , dotted, line width = 0.4](5.514,9.678)--(5.512,9.701)--(5.505,9.723)--(5.493,9.745)--(5.476,9.767)--(5.455,9.789)--(5.429,9.81)--(5.399,9.831)--(5.364,9.852)--(5.325,9.872)--(5.282,9.891)--(5.234,9.91)--(5.183,9.928)--(5.128,9.946)--(5.069,9.963)--(5.007,9.979)--(4.941,9.994)--(4.872,10.008)--(4.8,10.022)--(4.726,10.034)--(4.649,10.045)--(4.57,10.056)--(4.488,10.065)--(4.405,10.073)--(4.32,10.08)--(4.234,10.086)--(4.147,10.091)--(4.058,10.094)--(3.97,10.096)--(3.88,10.098)--(3.791,10.098)--(3.702,10.096)--(3.613,10.094)--(3.525,10.091)--(3.437,10.086)--(3.351,10.08)--(3.266,10.073)--(3.183,10.065)--(3.102,10.056)--(3.022,10.045)--(2.945,10.034)--(2.871,10.022)--(2.799,10.008)--(2.73,9.994)--(2.665,9.979)--(2.602,9.963)--(2.543,9.946)--(2.488,9.928)--(2.437,9.91)--(2.389,9.891)--(2.346,9.872)--(2.307,9.852)--(2.272,9.831)--(2.242,9.81)--(2.216,9.789)--(2.195,9.767)--(2.178,9.745)--(2.167,9.723)--(2.159,9.701)--(2.157,9.678);

\\draw [color=hhhhff , line width = 0.4](5.514,9.678)--(5.512,9.656)--(5.505,9.634)--(5.493,9.611)--(5.476,9.589)--(5.455,9.568)--(5.429,9.546)--(5.399,9.525)--(5.364,9.505)--(5.325,9.485)--(5.282,9.465)--(5.234,9.446)--(5.183,9.428)--(5.128,9.41)--(5.069,9.394)--(5.007,9.378)--(4.941,9.362)--(4.872,9.348)--(4.8,9.335)--(4.726,9.322)--(4.649,9.311)--(4.57,9.301)--(4.488,9.292)--(4.405,9.283)--(4.32,9.276)--(4.234,9.271)--(4.147,9.266)--(4.058,9.262)--(3.97,9.26)--(3.88,9.259)--(3.791,9.259)--(3.702,9.26)--(3.613,9.262)--(3.525,9.266)--(3.437,9.271)--(3.351,9.276)--(3.266,9.283)--(3.183,9.292)--(3.102,9.301)--(3.022,9.311)--(2.945,9.322)--(2.871,9.335)--(2.799,9.348)--(2.73,9.362)--(2.665,9.378)--(2.602,9.394)--(2.543,9.41)--(2.488,9.428)--(2.437,9.446)--(2.389,9.465)--(2.346,9.485)--(2.307,9.505)--(2.272,9.525)--(2.242,9.546)--(2.216,9.568)--(2.195,9.589)--(2.178,9.611)--(2.167,9.634)--(2.159,9.656)--(2.157,9.678);

\\fill[color = hhofof, opacity = 0.33](5.336,8.678)--(5.334,8.658)--(5.327,8.638)--(5.317,8.619)--(5.302,8.599)--(5.283,8.58)--(5.26,8.56)--(5.233,8.542)--(5.202,8.523)--(5.167,8.505)--(5.128,8.488)--(5.086,8.471)--(5.04,8.455)--(4.99,8.439)--(4.938,8.424)--(4.882,8.41)--(4.823,8.396)--(4.762,8.383)--(4.698,8.371)--(4.631,8.36)--(4.562,8.35)--(4.492,8.341)--(4.419,8.333)--(4.345,8.325)--(4.269,8.319)--(4.192,8.314)--(4.114,8.31)--(4.035,8.307)--(3.955,8.304)--(3.876,8.303)--(3.796,8.303)--(3.716,8.304)--(3.637,8.307)--(3.558,8.31)--(3.48,8.314)--(3.403,8.319)--(3.327,8.325)--(3.252,8.333)--(3.18,8.341)--(3.109,8.35)--(3.04,8.36)--(2.973,8.371)--(2.909,8.383)--(2.848,8.396)--(2.789,8.41)--(2.734,8.424)--(2.681,8.439)--(2.632,8.455)--(2.586,8.471)--(2.543,8.488)--(2.505,8.505)--(2.47,8.523)--(2.439,8.542)--(2.412,8.56)--(2.389,8.58)--(2.37,8.599)--(2.355,8.619)--(2.344,8.638)--(2.338,8.658)--(2.336,8.678)--(2.157,9.678)--(2.159,9.656)--(2.167,9.634)--(2.178,9.611)--(2.195,9.589)--(2.216,9.568)--(2.242,9.546)--(2.272,9.525)--(2.307,9.505)--(2.346,9.485)--(2.389,9.465)--(2.437,9.446)--(2.488,9.428)--(2.543,9.41)--(2.602,9.394)--(2.665,9.378)--(2.73,9.362)--(2.799,9.348)--(2.871,9.335)--(2.945,9.322)--(3.022,9.311)--(3.102,9.301)--(3.183,9.292)--(3.266,9.283)--(3.351,9.276)--(3.437,9.271)--(3.525,9.266)--(3.613,9.262)--(3.702,9.26)--(3.791,9.259)--(3.88,9.259)--(3.97,9.26)--(4.058,9.262)--(4.147,9.266)--(4.234,9.271)--(4.32,9.276)--(4.405,9.283)--(4.488,9.292)--(4.57,9.301)--(4.649,9.311)--(4.726,9.322)--(4.8,9.335)--(4.872,9.348)--(4.941,9.362)--(5.007,9.378)--(5.069,9.394)--(5.128,9.41)--(5.183,9.428)--(5.234,9.446)--(5.282,9.465)--(5.325,9.485)--(5.364,9.505)--(5.399,9.525)--(5.429,9.546)--(5.455,9.568)--(5.476,9.589)--(5.493,9.611)--(5.505,9.634)--(5.512,9.656)--(5.514,9.678)--cycle;
\\fill[color = hhhhff, opacity = 0.33](5.514,9.678)--(5.512,9.701)--(5.505,9.723)--(5.493,9.745)--(5.476,9.767)--(5.455,9.789)--(5.429,9.81)--(5.399,9.831)--(5.364,9.852)--(5.325,9.872)--(5.282,9.891)--(5.234,9.91)--(5.183,9.928)--(5.128,9.946)--(5.069,9.963)--(5.007,9.979)--(4.941,9.994)--(4.872,10.008)--(4.8,10.022)--(4.726,10.034)--(4.649,10.045)--(4.57,10.056)--(4.488,10.065)--(4.405,10.073)--(4.32,10.08)--(4.234,10.086)--(4.147,10.091)--(4.058,10.094)--(3.97,10.096)--(3.88,10.098)--(3.791,10.098)--(3.702,10.096)--(3.613,10.094)--(3.525,10.091)--(3.437,10.086)--(3.351,10.08)--(3.266,10.073)--(3.183,10.065)--(3.102,10.056)--(3.022,10.045)--(2.945,10.034)--(2.871,10.022)--(2.799,10.008)--(2.73,9.994)--(2.665,9.979)--(2.602,9.963)--(2.543,9.946)--(2.488,9.928)--(2.437,9.91)--(2.389,9.891)--(2.346,9.872)--(2.307,9.852)--(2.272,9.831)--(2.242,9.81)--(2.216,9.789)--(2.195,9.767)--(2.178,9.745)--(2.167,9.723)--(2.159,9.701)--(2.157,9.678)--(2.157,9.678)--(2.159,9.656)--(2.167,9.634)--(2.178,9.611)--(2.195,9.589)--(2.216,9.568)--(2.242,9.546)--(2.272,9.525)--(2.307,9.505)--(2.346,9.485)--(2.389,9.465)--(2.437,9.446)--(2.488,9.428)--(2.543,9.41)--(2.602,9.394)--(2.665,9.378)--(2.73,9.362)--(2.799,9.348)--(2.871,9.335)--(2.945,9.322)--(3.022,9.311)--(3.102,9.301)--(3.183,9.292)--(3.266,9.283)--(3.351,9.276)--(3.437,9.271)--(3.525,9.266)--(3.613,9.262)--(3.702,9.26)--(3.791,9.259)--(3.88,9.259)--(3.97,9.26)--(4.058,9.262)--(4.147,9.266)--(4.234,9.271)--(4.32,9.276)--(4.405,9.283)--(4.488,9.292)--(4.57,9.301)--(4.649,9.311)--(4.726,9.322)--(4.8,9.335)--(4.872,9.348)--(4.941,9.362)--(5.007,9.378)--(5.069,9.394)--(5.128,9.41)--(5.183,9.428)--(5.234,9.446)--(5.282,9.465)--(5.325,9.485)--(5.364,9.505)--(5.399,9.525)--(5.429,9.546)--(5.455,9.568)--(5.476,9.589)--(5.493,9.611)--(5.505,9.634)--(5.512,9.656)--(5.514,9.678)--cycle;
\\draw [color=black , dotted, line width = 0.4](3.836,9.678)--(5.514,9.678);
\\draw [color=black , line width = 0.4](3.836,0.278)--(5.336,8.678);
\\draw [color=black , line width = 0.4](3.836,0.278)--(2.336,8.678);
\\node at (3.411, 8.97) [align=left,below right ,black,,font= \\sf \\fontsize {0.398cm} {0.498cm} \\selectfont] {\\textbf{B}};
\\node at (5.362, 9.023) [align=left,below right ,black,,font= \\sf \\fontsize {0.398cm} {0.498cm} \\selectfont] {\\textbf{A}};
\\fill[color=black] (3.836,0.278) circle (0.053);
\\end{tikzpicture} \n\t \\end{minipage}`
        }
        texteCorr = numAlpha(0) + ' Les triangles SBA et SHL sont semblables car les droites (BA) et (HL) sont parallèles dans le plan du triangle SHL.<br>'
        texteCorr += ' La tangente de l\'angle $\\widehat{HSL}$ est égale dans le triangle SHL à $\\dfrac{\\text{HL}}{\\text{SH}}$ et dans le triangle SBA à $\\dfrac{\\text{BA}}{\\text{SB}}$.<br>'
        texteCorr += ' d\'où $\\dfrac{\\text{HL}}{\\text{SH}}=\\dfrac{\\text{BA}}{\\text{SH}-\\text{BH}}$ '
        texteCorr += ' et l\'égalité des produits en croix nous donne : $\\text{HL}\\left(\\text{SH}-\\text{BH} \\right) =\\text{BA}\\times \\text{SH}$.<br>'
        texteCorr += ` Soit avec les données numériques : $${texNombre(r, 1)}\\left(\\text{SH}-${texNombre(h3, 1)}\\right)=${texNombre(r2, 1)}\\times \\text{SH}$.<br>`
        texteCorr += `On en déduit que SH$\\left(${texNombre(r, 1)}-${texNombre(r2, 1)}\\right)=${texNombre(r, 1)}\\times${texNombre(h3, 1)}$.<br>`
        texteCorr += `D'où SH $=\\dfrac{${texNombre(r.mul(h3), 2)}}{${texNombre(r.sub(r2), 1)}}=${texNombre(h1, 1)}$ dm ( SB = $${texNombre(h2, 1)}$ dm).<br>`

        texteCorr += numAlpha(1) + ` Le volume du cône est $\\dfrac{A_\\text{base}}{3}\\times \\text{hauteur}$ dm${texteExposant(3)} $= \\dfrac{${texNombre(r.pow(2), 2)}\\pi}{3} \\times ${texNombre(h1, 1)}$ dm${texteExposant(3)} $= \\dfrac{${texNombre(r.mul(r).mul(h1), 3)}}{3}\\pi$ dm${texteExposant(3)} $\\approx ${texNombre(r.mul(r).mul(pi).mul(h1).div(3), 3)}$ dm${texteExposant(3)}.<br>`
        texteCorr += numAlpha(2) + ' Le seau est un tronc de cône. Pour calculer son volume, on va calculer le volume du cône réduit de hauteur SB et le soustraire du volume du cône de hauteur SH.<br>'
        texteCorr += ` Le cône de hauteur SB est une réduction du cône de hauteur SH. Le coefficient de cette réduction est : $\\dfrac{${texNombre(r2, 1)}}{${texNombre(r, 1)}}`
        if (!Number.isInteger(r) || pgcd(r2.mul(10), r * 10) > 1) { texteCorr += `=${texFractionReduite(r2.mul(10), r.mul(10))}$.<br>` } else { texteCorr += '.$<br>' }
        texteCorr += `Dans une réduction de coefficient k, les volumes sont multipliés par k${texteExposant(3)}.<br>`
        texteCorr += `Donc le volume du cône de hauteur SB est : $\\left(${texFractionReduite(r2.mul(10), r.mul(10))}\\right)^3 \\times \\dfrac{${texNombre(r.mul(r).mul(h1), 3)}}{3}\\pi$ dm${texteExposant(3)} $\\approx ${texNombre(pi.mul(h2.div(h1).pow(3)).mul(r.pow(2).mul(h1)).div(3), 3)}$ dm${texteExposant(3)} '.<br>`
        texteCorr += 'Le volume du tronc de cône est : '
        texteCorr += `$V_\\text{Cône} - V_\\text{CôneRéduit}$<br>Soit : <br>$\\dfrac{${texNombre(r.mul(r).mul(h1), 3)}}{3}\\pi$ dm${texteExposant(3)}$ - \\left(${texFractionReduite(r2.mul(10), r.mul(10))}\\right)^3 \\times \\dfrac{${texNombre(r.mul(r).mul(h1), 3)}}{3}\\pi$ dm${texteExposant(3)} `
        texteCorr += `$ = \\left(1-\\left(${texFractionReduite(r2.mul(10), r.mul(10))}\\right)^3\\right)\\times \\dfrac{${texNombre(r.mul(r).mul(h1), 3)}}{3}\\pi$ dm${texteExposant(3)} `
        texteCorr += `$ = \\left(1-\\dfrac{${fractionSimplifiee(r2.mul(10), r.mul(10))[0] ** 3}}{${fractionSimplifiee(r2.mul(10), r.mul(10))[1] ** 3}}\\right)\\times \\dfrac{${texNombre(r.mul(r).mul(h1), 3)}}{3}\\pi$ dm${texteExposant(3)} `
        texteCorr += `$ = \\dfrac{${fractionSimplifiee(r2.mul(10), r.mul(10))[1] ** 3 - fractionSimplifiee(r2.mul(10), r.mul(10))[0] ** 3}}{${fractionSimplifiee(r2.mul(10), r.mul(10))[1] ** 3}}\\times \\dfrac{${texNombre(r.mul(r).mul(h1), 3)}}{3}\\pi$ dm${texteExposant(3)} `
        kprime = new Decimal(r2).div(r).pow(3)
        texteCorr += `$ \\approx ${texNombre(r.pow(2).mul(h1).mul(pi).div(3).mul(kprime.sub(1).mul(-1)), 3)}$ dm${texteExposant(3)}<br>`
        c = h3.div(2)
        kprime = c.plus(h2).div(h2)
        if (context.isHtml) {
          texteCorr += numAlpha(3) + ` Il faut fixer HL à ${texNombre(r * 10)} cm ; BA à ${texNombre(r2.mul(10), 0)} cm ; BH à ${texNombre(h3.mul(10), 0)} cm et la hauteur d'eau à ${texNombre(h1.sub(h2).mul(5), 1)} cm.<br>`
          texteCorr += `La lecture de $ y = V(x)$ nous donne un volume d'eau d'environ $${texNombre(kprime.pow(3).sub(1).mul(r2.pow(2)).mul(h2).mul(pi).div(3), 1)}$ dm${texteExposant(3)} soit environ $${texNombre(kprime.pow(3).sub(1).mul(r2.pow(2)).mul(h2).mul(pi).div(3), 0)}$ litres d'eau.<br>`
          texteCorr += numAlpha(4)
        } else { texteCorr += numAlpha(3) }
        texteCorr += ' Nous allons déterminer le volume du cône de hauteur SE, puis nous soustrairons le volume du cône de hauteur SB pour obtenir le volume d\'eau.<br>'
        texteCorr += ` Le cône de hauteur SE est une réduction du cône de hauteur SH. Le coefficient de cette réduction est : $${texFractionReduite(c.add(h2).mul(100), h1.mul(100))}$.<br>`
        texteCorr += `Donc le volume $V$ du cône de hauteur SE est : $\\left(${texFractionReduite(h1.add(h2).mul(50), h1.mul(100))}\\right)^3 \\times \\dfrac{${texNombre(r.mul(r).mul(h1), 3)}}{3}\\pi$ dm${texteExposant(3)} $\\approx ${texNombre(r.pow(2).mul(pi).mul(h2.plus(c).div(h1).pow(3)).mul(h1).div(3), 3)}$ dm${texteExposant(3)}.<br>`
        texteCorr += 'Notons $V\'$ le volume du cône de hauteur SB calculé à la question ' + numAlpha(2) + '<br> Le volume d\'eau est donc : '

        texteCorr += `$V-V' \\approx ${texNombre(pi.div(3).mul(r.pow(2)).mul(h1).mul(h2.plus(c).div(h1).pow(3)), 3)}$ dm${texteExposant(3)}$ - ${texNombre(pi.div(3).mul(h2.div(h1).pow(3).mul(r.pow(2))).mul(h1), 3)}$ dm${texteExposant(3)} $\\approx ${texNombre(kprime.pow(3).sub(1).mul(r2.pow(2)).mul(h2).mul(pi).div(3), 1)}$ dm${texteExposant(3)}.<br>`
        this.MG32codeBase64 = codeBase64
        this.mg32init = (mtg32App, idDoc) => {
          mtg32App.calculate(idDoc, true)
          return mtg32App.display(idDoc)
        }
        break
      case 5: // Un problème avec un cône Vanille Chocolat.
        r = new Decimal(randint(20, 28)).div(10)
        h1 = new Decimal(randint(20, 28)).div(2)
        h2 = new Decimal(randint(1, 3))

        if (this.sup2 < 3) {
          if (parseInt(this.sup2) === 1) { // coefficient de réduction décimal
            while (!h2.div(h1).mul(10).eq(h2.div(h1).mul(10).round())) {
              r = new Decimal(randint(20, 28)).div(10)
              h1 = new Decimal(randint(20, 28)).div(2)
              h2 = new Decimal(randint(1, 3))
            }
          } else { // coefficient de réduction rationnel
            while (h2.div(h1).mul(10).eq(h2.div(h1).mul(10).round())) {
              r = new Decimal(randint(20, 28)).div(10)
              h1 = new Decimal(randint(20, 28)).div(2)
              h2 = new Decimal(randint(1, 3))
            }
          }
        }
        r2 = r.mul(h2).div(h1)
        codeBase64 = 'TWF0aEdyYXBoSmF2YTEuMAAAABI+TMzNAANmcmH###8BAP8BAAAAAAAAAAAFKgAAAuAAAAAAAAAAAAAAAAAAAAET#####wAAAAEACkNDYWxjQ29uc3QA#####wACcGkAFjMuMTQxNTkyNjUzNTg5NzkzMjM4NDb#####AAAAAQAKQ0NvbnN0YW50ZUAJIftURC0Y#####wAAAAEAD0NWYXJpYWJsZUJvcm5lZQD#####AANhbmc#6SH7VEQtGAAAAAAAAAAAQBkh+1RELRg#qZmZmZmZmgAAATAABDIqcGkABDAuMDX#####AAAAAQAKQ1BvaW50QmFzZQD#####AQAAAAAQAAAAQAgAAAAAAAAAAAAAAAAAAAUAAUB#eAAAAAAAQHqoUeuFHrj#####AAAAAQAHQ0NhbGN1bAD#####AAVtaW5pMQADMC4yAAAAAT#JmZmZmZmaAAAABAD#####AAVtYXhpMQABMgAAAAFAAAAAAAAAAP####8AAAABABRDSW1wbGVtZW50YXRpb25Qcm90bwD#####AAdDdXJzZXVyAAAABQAAAAUAAAADAAAAAwAAAAQAAAAC#####wAAAAEAFENEcm9pdGVEaXJlY3Rpb25GaXhlAAAAAAUBAAAAABAAAAEAAQAAAAIBP#AAAAAAAAD#####AAAAAQAPQ1BvaW50TGllRHJvaXRlAQAAAAUBAAAAABAAAADACAAAAAAAAD#wAAAAAAAABQABQEuAAAAAAAAAAAAG#####wAAAAEAC0NIb21vdGhldGllAAAAAAUAAAAC#####wAAAAEACkNPcGVyYXRpb24D#####wAAAAEAD0NSZXN1bHRhdFZhbGV1cgAAAAMAAAAJAQAAAAoAAAADAAAACgAAAAT#####AAAAAQALQ1BvaW50SW1hZ2UAAAAABQEAAAAADQACTzEAwBAAAAAAAABAEAAAAAAAAAUAAAAABwAAAAgAAAAIAAAAAAUAAAACAAAACQMAAAAJAQAAAAE#8AAAAAAAAAAAAAoAAAADAAAACQEAAAAKAAAABAAAAAoAAAADAAAACwAAAAAFAQAAAAANAAJJNQDAAAAAAAAAAEAIAAAAAAAABQAAAAAHAAAACv####8AAAABAAhDU2VnbWVudAEAAAAFAQAAAAAQAAABAQEAAAACAAAABwAAAAcBAAAABQEAAAABEAACazEAwAAAAAAAAABAAAAAAAAAAAEAAT#aw32sN9rDAAAADP####8AAAACAA9DTWVzdXJlQWJzY2lzc2UBAAAABQAEem9vbQAAAAkAAAALAAAADf####8AAAABAA9DVmFsZXVyQWZmaWNoZWUBAAAABQEAAAAAAAAAAAAAAADAGAAAAAAAAAAAAA0PAAH###8AAAABAAAAAgAAAAEAAAAAAAAAAAAAAAACAAAADgAAAAMA#####wH#AAAAEAABWgAAAAAAAAAAAEAIAAAAAAAABQABQHmoAAAAAABAd2hR64UeuAAAAAgA#####wAAABAAAAAKAAAADgAAAAYA#####wH#AAABEAAAAQEBAAAAEAA#8AAAAAAAAAAAAAcA#####wH#AAAAEAABTQAAAAAAAAAAAEAIAAAAAAAABQABwEgAAAAAAAAAAAASAAAACwD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAAEwAAABEAAAADAP####8BAAAAAQ8AAk8yAQUAAUCA3AAAAAAAQICEKPXCj1wAAAAGAP####8BAAAAARAAAAEAAQAAABUAP#AAAAAAAAAAAAAHAP####8BAAAAAQ8AAkoyAQUAAMBAAAAAAAAAAAAAFv####8AAAABAAlDTG9uZ3VldXIA#####wAAABUAAAAXAAAAAwD#####AAAAAAAPAAFPAMAYAAAAAAAAQCQAAAAAAAAFAAFAYpAAAAAAAEBIQo9cKPXDAAAABgD#####AQAAAAAQAAABAAEAAAAZAUAD6BRQ79ycAAAABwD#####Af8AAAAQAAJJIgAAAAAAAAAAAEAIAAAAAAAABQABQDF7TwMpFiAAAAAaAAAABAD#####AAJoMQACMTAAAAABQCQAAAAAAAAAAAAEAP####8AAmgyAAE0AAAAAUAQAAAAAAAAAAAABAD#####AAFyAAMzLjUAAAABQAwAAAAAAAD#####AAAAAQARQ1N5bWV0cmllQ2VudHJhbGUA#####wAAABUAAAADAP####8BAAAAAQ8AAk8zAQUAAUCSQgAAAAAAQHe4UeuFHrcAAAAGAP####8BAAAAABAAAAEAAQAAACABQAPoFFDv3JwAAAADAP####8BAAAAAQsAAk80AQUAAUCSVgAAAAAAQH5YUeuFHrgAAAAGAP####8BAAAAABAAAAEAAQAAACIBQAPoFFDv3JwAAAAQAP####8AAAAZAAAACwD#####AQB#AAALAAJXNADANQAAAAAAAMAUAAAAAAAABQAAAAAXAAAAH#####8AAAABAAxDVHJhbnNsYXRpb24A#####wAAABUAAAAXAAAACwD#####AQAAAAALAAJXNwBAAAAAAAAAAAAAAAAAAAAABQAAAAAgAAAAJv####8AAAABAAlDQ2VyY2xlT0EA#####wF#f38BAQAAACAAAAAn#####wAAAAEAEENJbnREcm9pdGVDZXJjbGUA#####wAAACEAAAAo#####wAAAAEAEENQb2ludExpZUJpcG9pbnQA#####wEAAAAADQACSTMBBQABAAAAKf####8AAAABAA9DUG9pbnRMaWVDZXJjbGUA#####wEAAAABCwACSzMBAQABQBX9VSbZZwcAAAAo#####wAAAAIAE0NNZXN1cmVBbmdsZU9yaWVudGUA#####wAIYW5ndGhldGEAAAAqAAAAIAAAACsAAAAEAP####8ABXRoZXRhAAhhbmd0aGV0YQAAAAoAAAAsAAAABAD#####AAN4JzEACy1zaW4odGhldGEp#####wAAAAEADENNb2luc1VuYWlyZf####8AAAACAAlDRm9uY3Rpb24DAAAACgAAAC0AAAAEAP####8AA3gnMgALLWNvcyh0aGV0YSkAAAAXAAAAGAQAAAAKAAAALQAAABUA#####wEAAAAACwACVzEAwAAAAAAAAABAAAAAAAAAAAUAAUATXOOpPArvAAAAKAAAABYA#####wAFYW5nbGUAAAAqAAAAIAAAADD#####AAAAAQASQ0FyY0RlQ2VyY2xlRGlyZWN0AP####8Bf39#AQEAAAAVAAAAFwAAACUAAAAVAP####8BAAAAAQsAAksyAQEAAT+3ICjs75hDAAAAMgAAABYA#####wAGYW5ncGhpAAAAFwAAABUAAAAzAAAABAD#####AANwaGkACXBpK2FuZ3BoaQAAAAkAAAAACgAAAAAAAAAKAAAANAAAAAQA#####wADeScxABNjb3ModGhldGEpKnNpbihwaGkpAAAACQIAAAAYBAAAAAoAAAAtAAAAGAMAAAAKAAAANQAAAAQA#####wADeScyABQtc2luKHRoZXRhKSpzaW4ocGhpKQAAABcAAAAJAgAAABgDAAAACgAAAC0AAAAYAwAAAAoAAAA1#####wAAAAEAF0NNZXN1cmVBbmdsZUdlb21ldHJpcXVlAP####8AAAAXAAAAFQAAACUAAAAEAP####8ABHBsYXQABkoyTzJXNAAAAAoAAAA4AAAABAD#####AAVkcm9pdAAGcGxhdC8yAAAACQMAAAAKAAAAOQAAAAFAAAAAAAAAAAAAAAwA#####wEAAAAAEAAAAQABAAAAFQAAABcAAAAMAP####8BAAAAABAAAAEAAQAAACAAAAAqAAAADAD#####AQAAAAAQAAABAAEAAAAgAAAAK#####8AAAACABNDTWFycXVlQW5nbGVPcmllbnRlAP####8BfwAAAAIAAAAAQDiyu8xLZZ0AAAAqAAAAIAAAACsB#####wAAAAEADENCaXNzZWN0cmljZQD#####AX8AAAAQAAABAQEAAAAqAAAAIAAAACsAAAAHAP####8BfwAAABAAAAEFAAFAebYKC41k5QAAAD######AAAAAgAGQ0xhdGV4AP####8BfwAAAMAUAAAAAAAAwCYAAAAAAAAAAABAEQAAAAAAAAAAAAAAAAABAAAAAAAAAAAAClx2YXJ0aGV0YSAAAAAMAP####8BAAAAABAAAAEAAQAAABUAAAAzAAAACAD#####AAAAIgAAABgEAAAACgAAADUAAAAbAP####8BAAD#AAIAAAAAQDdS5Q2zo6IAAAAXAAAAFQAAADMBAAAAHAD#####AQAA#wAQAAABAQEAAAAXAAAAFQAAADMAAAAHAP####8BAAD#ABAAAAEFAAFAd7hgWcShNQAAAEUAAAAdAP####8BAAD#AAAAAAAAAAAAwBQAAAAAAAAAAABGEQAAAAAAAQAAAAEAAAABAAAAAAAAAAAAB1x2YXJwaGkAAAAEAP####8AAWsACHNpbihwaGkpAAAAGAMAAAAKAAAANQAAAAQA#####wAKdGVzdFBoaU51bAAnMS8oKHBoaT0wKSsoYWJzKHBoaS1wbGF0KTwwLjAwMDAwMDAwMSkpAAAACQMAAAABP#AAAAAAAAAAAAAJAAAAAAkIAAAACgAAADUAAAABAAAAAAAAAAAAAAAJBAAAABgAAAAACQEAAAAKAAAANQAAAAoAAAA5AAAAAT4RLgvoJtaVAAAACAD#####AAAAGQAAAAoAAABJAAAABgD#####AQAAAAEQAAABAAEAAAAiAD#wAAAAAAAAAAAABwD#####AQAAAAELAAJKNAEFAAHAS4AAAAAAAAAAAEsAAAASAP####8BZmZmAAEAAAAiAAAATAAAABUA#####wEAAAAAEAAAAQUAAT#wl+m6eQJhAAAATQAAAAYA#####wEAAAAAEAAAAQABAAAATgBAA+gUUO#cnP####8AAAABABBDSW50RHJvaXRlRHJvaXRlAP####8BAAAAABAAAAEFAAAAACMAAABPAAAAEwD#####AAAAIwAAAE0AAAAUAP####8BAAAAAA0AAkk0AQUAAQAAAFH#####AAAAAgAHQ1JlcGVyZQD#####AAAAAAEBAAAAIgAAAFIAAABMAAAAAAAAAQAAAAAAAAAAAAAAAQAAAAAAAAAAAAAAAT#wAAAAAAAAAAAAAT#wAAAAAAAAAAAACwD#####AQAAAAAQAAABBQAAAABMAAAAQwAAAAgA#####wAAAFAAAAAYBAAAAAoAAAA1AAAACwD#####AQAAAAAQAAABBQAAAABOAAAAVf####8AAAACAA1DTGlldURlUG9pbnRzAP####8BAH9#AQEAAABWAAAAZAAAAAAATgAAAAUAAABOAAAATwAAAFAAAABVAAAAVv####8AAAABAAhDVmVjdGV1cgD#####AQAA#wAQAAABAAEAAAAiAAAAVAD#####AAAAAQAQQ1BvaW50RGFuc1JlcGVyZQD#####AQAAAAAQAAABBQAAAABTAAAACgAAAC4AAAAKAAAANgAAACIA#####wEAAAAAEAAAAQUAAAAAUwAAAAoAAAAvAAAACgAAADcAAAAhAP####8B#wAAABAAAAEAAQAAACIAAABZAAAAACEA#####wEAfwAAEAAAAQABAAAAIgAAAFoAAAAAIAD#####AWZmZgEBAAAAWQAAAGQAAAAAACsAAAAGAAAAKwAAACwAAAAtAAAALgAAADYAAABZ#####wAAAAEADENTdXJmYWNlTGlldQD#####AX9#fwAAAAUAAABdAAAAIwD#####AX9#fwAAAAUAAABXAAAAEgD#####Af8AAAEBAAAAGQAAABv#####AAAAAQANQ0RlbWlEcm9pdGVPQQD#####Af8AAAANAAABAQEAAAAQAAAAE#####8AAAABAA5DUG9pbnRMaWVQb2ludAD#####Af8AAAAQAAFVAEAgAAAAAAAAwCoAAAAAAAAFAAAAABQAAAANAP####8AAXUAAAAQAAAAEwAAAGL#####AAAAAQARQ1BvaW50UGFyQWJzY2lzc2UA#####wH#AAAAEAACSTIAAAAAAAAAAABACAAAAAAAAAUAAAAAGQAAABsAAAAKAAAAYwAAACUA#####wEAAAAACwACSTEAwBAAAAAAAABAEAAAAAAAAAUAAAAAZP####8AAAABAAlDRHJvaXRlQUIA#####wEAAAAADQAAAQABAAAAGQAAAGX#####AAAAAQAWQ0Ryb2l0ZVBlcnBlbmRpY3VsYWlyZQD#####AQAAAAAQAAABAAEAAAAZAAAAZgAAABIA#####wEAAAAAAQAAABkAAABlAAAAEwD#####AAAAZwAAAGgAAAAUAP####8BAAAAAAsAAkoxAMAoAAAAAAAAwBAAAAAAAAAFAAIAAABpAAAAHwD#####AICAgAEBAAAAGQAAAGUAAABqAAAAAAAAAQAAAAAAAAAAAAAAAQAAAAAAAAAAAAAAAT#wAAAAAAAAAAAAAT#wAAAAAAAAAAAAIgD#####AQAAAAAPAAFJAD#wAAAAAAAAQBAAAAAAAAAFAAAAAGsAAAAKAAAALgAAAAoAAAA2AAAAIgD#####AQAAAAAPAAFKAQUAAAAAawAAAAoAAAAvAAAACgAAADcAAAAkAP####8BAAAAAA0AAAEBAQAAABkAAABsAAAAIgD#####AQAAAAAPAAFLAEAQAAAAAAAAwC4AAAAAAAAFAAAAAGsAAAABAAAAAAAAAAAAAAAYBAAAAAoAAAA1AAAAJAD#####AQAAAAANAAABAQEAAAAZAAAAbwAAACQA#####wEAAAAADQAAAQEBAAAAGQAAAG0AAAAhAP####8B#wAAABAAAAEAAQAAABkAAABsAAAAACEA#####wEAfwAAEAAAAQABAAAAGQAAAG0AAAAAIQD#####AQAA#wAQAAABAAEAAAAZAAAAbwD#####AAAAAQAPQ1N5bWV0cmllQXhpYWxlAP####8AAABw#####wAAAAEAEUNNYWNyb0Rpc3Bhcml0aW9uAP####8BAAD#Af####8NQH3AAAAAAABAgkAAAAAAAAIBzMz#AAAAAAAAAAAAAAABAAAAAAAAAAAAEyhPLEksSixLKSBpbnZpc2libGUAAAAAAAkAAABxAAAAbgAAAHAAAAByAAAAcwAAAHQAAABtAAAAbAAAAG######AAAAAQAQQ01hY3JvQXBwYXJpdGlvbgD#####AQAA#wH#####DUB+cAAAAAAAQIMYAAAAAAACAczM#wAAAAAAAAAAAAAAAQAAAAAAAAAAABEoTyxJLEosSykgdmlzaWJsZQAAAAAACQAAAHEAAABuAAAAcAAAAHIAAABzAAAAdAAAAG0AAABsAAAAbwAAAAAfAP####8AgICAAQEAAAAZAAAAbAAAAG0AAAAAAAABAAAAAAAAAAAAAAABAAAAAAAAAAAAAAABP#AAAAAAAAAAAAABP#AAAAAAAAAAAAAiAP####8B2NjYABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAABrAAAACgAAAB4AAAABAAAAAAAAAAAAAAAiAP####8BAAAAABAAAUIAAAAAAAAAAABACAAAAAAAAAUAAAAAeAAAAAoAAAAeAAAAAQAAAAAAAAAAAAAAJQD#####AQAAAAAPAAFBAQUAAAAAegAAAA0A#####wAEYWJzMQAAABkAAABsAAAAewAAAAQA#####wADUmF5AARhYnMxAAAACgAAAHwAAAAmAP####8BAAAAABAAAAEFAAAAABkAAABsAAAACQIAAAAKAAAAfQAAABgEAAAACgAAADEAAAAmAP####8BAAAAABAAAAEFAAAAABkAAABtAAAACQIAAAAKAAAAfQAAABgDAAAACgAAADEAAAARAP####8AAAAZAAAAfgAAAAsA#####wEAAAAAEAAAAQUAAAAAfwAAAIAAAAAgAP####8Af39#AQEAAACBAAAAeAEAAAAAMAAAAAYAAAAwAAAAMQAAAH4AAAB#AAAAgAAAAIEAAAAjAP####8A##8AAAAABQAAAIIAAAAiAP####8BAAAAABAAAAEFAAAAAGsAAAABAAAAAAAAAAAAAAAJAQAAAAEAAAAAAAAAAAAAAAoAAAB9AAAAEgD#####AQAAAAEBAAAAGQAAAIQAAAATAP####8AAABxAAAAhQAAABQA#####wEAAAAAEAAAAQUAAQAAAIYAAAALAP####8B#wD#ABAAAAEFAAAAAIcAAABKAAAACwD#####Af8A#wAQAAABBQAAAACIAAAAJAAAAAwA#####wEAAAAAEAAAAQACAAAAiAAAAIkAAAAHAP####8BAAAAABAAAAEFAAE#tLY8pd6vvwAAAIr#####AAAAAQAOQ09iamV0RHVwbGlxdWUA#####wAAAAAAAACKAAAADQD#####AAFhAAAAGQAAAGwAAAB7AAAAIgD#####AWZmZgAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAAeAAAAAkCAAAACgAAAI0AAAAYBAAAAAoAAAABAAAACQIAAAAKAAAAjQAAABgDAAAACgAAAAEAAAAfAP####8A5ubmAAEAAAAZAAAAbAAAAG8AAAAAAAABAAAAAAAAAAAAAAABAAAAAAAAAAAAAAABP#AAAAAAAAAAAAABP#AAAAAAAAAAAAAiAP####8BAAAAABAAAlMiAMA5AAAAAAAAwC4AAAAAAAAFAAAAAI8AAAABAAAAAAAAAAAAAAAKAAAAHAAAACUA#####wEAAAAADwABUwDARIAAAAAAAMAiAAAAAAAABQAAAACQAAAADQD#####AAVhYnMxMQAAABkAAABqAAAAkQAAAAQA#####wABcwAFYWJzMTEAAAAKAAAAkgAAACwA#####wAAAAAAAACR#####wAAAAEADkNUZXN0RXhpc3RlbmNlAP####8ACEV4aXN0RGVzAAAAkgAAAAQA#####wAKdGVzdFNFZ2FsTwAOMS8oMS1FeGlzdERlcykAAAAJAwAAAAE#8AAAAAAAAAAAAAkBAAAAAT#wAAAAAAAAAAAACgAAAJUAAAAIAP####8AAAAZAAAACgAAAJYAAAAEAP####8AA3knMAALa14yKlJheV4yL3MAAAAJAwAAAAkC#####wAAAAEACkNQdWlzc2FuY2UAAAAKAAAASAAAAAFAAAAAAAAAAAAAAC4AAAAKAAAAfQAAAAFAAAAAAAAAAAAAAAoAAACTAAAABAD#####AAN4JzAAFHJhYyhSYXleMi15JzBeMi9rXjIpAAAAGBIAAAAJAQAAAC4AAAAKAAAAfQAAAAFAAAAAAAAAAAAAAAkDAAAALgAAAAoAAACYAAAAAUAAAAAAAAAAAAAALgAAAAoAAABIAAAAAUAAAAAAAAAAAAAAIgD#####Af8AAAAQAAABBQAAAABrAAAACgAAAJkAAAAKAAAAmAAAAAsA#####wH#AAAAEAAAAQUAAAAAmgAAAHUAAAAGAP####8BAAAAABAAAAEBAQAAAJoAP#MzMzMzMzMAAAAGAP####8BAAAAABAAAAEBAQAAAJsAP#MzMzMzMzMAAAATAP####8AAACdAAAAhQAAABQA#####wEAAAAAEAAAAQUAAgAAAJ4AAAATAP####8AAACcAAAAhQAAABQA#####wEAAAAAEAAAAQUAAgAAAKAAAAAZAP####8BAAAAAQEAAAAZAAAAnwAAAKEAAAAVAP####8BAAAAAAsAAlczAMAkAAAAAAAAQBgAAAAAAAAFAAE#0#omyqGlpQAAAKL#####AAAAAQANQ1BvaW50UHJvamV0ZQD#####AQAAAAALAAJXMgDALgAAAAAAAEAUAAAAAAAABQAAAACjAAAAZgAAACYA#####wEAAAAACwACVzUAwCAAAAAAAABAIAAAAAAAAAUAAAAApAAAAKP#####AAAAAQANQ0ZvbmN0aW9uM1ZhcgAAAAAJAgAAAAkHAAAACgAAADUAAAABAAAAAAAAAAAAAAAJBgAAAAoAAAA1AAAACgAAADoAAAAKAAAASAAAAAkBAAAAAQAAAAAAAAAAAAAACgAAAEgAAAAEAP####8ACHRlc3RTaW50ABYxLyhhYnMocyk8PWFicyhrKSpSYXkpAAAACQMAAAABP#AAAAAAAAAAAAAJBgAAABgAAAAACgAAAJMAAAAJAgAAABgAAAAACgAAAEgAAAAKAAAAfQAAAAwA#####wAAAAAAEAAAAQACAAAAkQAAAJoAAAAMAP####8AAAAAABAAAAEAAgAAAJEAAACbAAAADAD#####AX9#fwAQAAABAAEAAACRAAAApQAAAAcA#####wEAAAAACwACVzYBBQABP+kwagu4xeQAAACpAAAAIAD#####AX9#fwABAAAAqgAAAFAAAAAAAKMAAAAFAAAAowAAAKQAAAClAAAAqQAAAKr#####AAAAAgASQ0xpZXVPYmpldFBhclB0TGllAP####8A2NjYAAAAqwAAAAFAJAAAAAAAAAAAAKoAAAACAAAAqgAAAKsAAAAgAP####8BAAAAAAIAAAClAAAAeAAAAAAAowAAAAMAAACjAAAApAAAAKUAAAAIAP####8AAAAZAAAACgAAAKYAAAALAP####8B#wD#ABAAAAEFAAAAAJEAAACuAAAADAD#####AX9#fwAQAAABAAEAAACvAAAAgQAAADEA#####wB#f38AAACwAAAAAUA1AAAAAAAAAAAAMAAAAAcAAAAwAAAAMQAAAH4AAAB#AAAAgAAAAIEAAACwAAAABwD#####AX9#fwAQAAABBQABP+jGPF4uJ0YAAACwAAAAIAD#####AX9#fwABAAAAsgAAAFABAAAAADAAAAAIAAAAMAAAADEAAAB+AAAAfwAAAIAAAACBAAAAsAAAALIAAAAxAP####8Af39#AAAAswAAAAFAJAAAAAAAAAAAALIAAAACAAAAsgAAALMAAAAsAP####8AAAAAAAAArQAAAAgA#####wAAAJEAAAAKAAAApgAAAAsA#####wH#AAAAEAAAAQUAAAAAgQAAALYAAAAgAP####8BAAAAAAIAAAC3AAAAZAEAAAAAMAAAAAcAAAAwAAAAMQAAAH4AAAB#AAAAgAAAAIEAAAC3AAAALAD#####AAAAAAAAALgAAAALAP####8B#wAAABAAAAEFAAAAAIQAAACXAAAAEgD#####AQAAAAACAAAAGQAAALoAAAAVAP####8BAAAAABAAAAEFAAFAAnKZ09yUFQAAALsAAAAMAP####8Bf39#ABAAAAEAAQAAABkAAAC8AAAABwD#####AX9#fwAQAAABBQABP+nN99SrrBcAAAC9AAAAEgD#####AX9#fwABAAAAGQAAAL4AAAAxAP####8Af39#AAAAvQAAAAFANAAAAAAAAAAAALwAAAACAAAAvAAAAL0AAAAxAP####8Af39#AAAAvwAAAAFAJAAAAAAAAAAAAL4AAAACAAAAvgAAAL8AAAAsAP####8AAAAAAAAAuwAAAAwA#####wEAAAAAEAAAAQACAAAAiQAAAJEAAAAHAP####8Bf39#ABAAAAEFAAE#wdH0IWEZJQAAAMMAAAAGAP####8Bf39#ABAAAAEAAQAAAMQBP#MzMzMzMzMAAAAMAP####8BAAAAABAAAAEAAgAAAJEAAACIAAAAHgD#####AX9#fwAQAAABBQAAAADFAAAAxgAAAAwA#####wF#f38AEAAAAQABAAAAxAAAAMcAAAAxAP####8Af39#AAAAyAAAAAFAJAAAAAAAAAAAAMQAAAAEAAAAxAAAAMUAAADHAAAAyAAAAAwA#####wF#f38AEAAAAQABAAAAkQAAAIsAAAAxAP####8Af39#AAAAygAAAAFAJAAAAAAAAAAAAIsAAAACAAAAiwAAAMoAAAAsAP####8AAAAAAAAAwwAAACwA#####wAAAAAAAADGAAAADAD#####AQAAAAAQAAABAQEAAACRAAAAjv####8AAAACABVDTGlldU9iamV0UGFyVmFyaWFibGUA#####wC9vb0AAADOAAAAAUA5AAAAAAAAAAAAAQAAAAMAAAABAAAAjgAAAM4AAAAiAP####8AAAAAABAAAk8nAMA5AAAAAAAAwCoAAAAAAAAFAAAAAI8AAAABAAAAAAAAAAAAAAAJAQAAAAoAAAAcAAAACgAAAB3#####AAAAAQAQQ0Ryb2l0ZVBhcmFsbGVsZQD#####Aebm5gAQAAABAAEAAADQAAAAbgAAAAwA#####wDm5uYAEAAAAQABAAAAkQAAAH4AAAAeAP####8BpKSkABAAAlAiAAAAAAAAAAAAQAgAAAAAAAAFAAAAANEAAADSAAAAMwD#####Aebm5gAQAAABAAEAAADQAAAAcQAAAAwA#####wDm5uYAEAAAAQABAAAAfwAAAJEAAAAeAP####8BpKSkABAAAlEiAMA7AAAAAAAAwCIAAAAAAAAFAAAAANQAAADVAAAAEQD#####AAAA0AAAANMAAAALAP####8BpKSkABAAAlAnAAAAAAAAAAAAQAgAAAAAAAAFAAAAANYAAADXAAAAIAD#####AKSkpAEBAAAA2AAAAHgBAAAAACsAAAAeAAAAKwAAACwAAAAtAAAALgAAAC8AAAA2AAAANwAAAGwAAABtAAAAbgAAAHEAAAB4AAAAegAAAHsAAAB8AAAAfQAAAH4AAAB#AAAAjwAAAJAAAACRAAAA0AAAANEAAADSAAAA0wAAANQAAADVAAAA1gAAANcAAADYAAAAIwD#####AP8AAAAAAAUAAADZAAAAEwD#####AAAAZwAAAGAAAAAUAP####8B#wAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQABAAAA2wAAABQA#####wH#AAAAEAACSiIAAAAAAAAAAABACAAAAAAAAAUAAgAAANsAAAAfAP####8A5ubmAAEAAAAZAAAAGwAAAN0AAAAAAAABAAAAAAAAAAAAAAABAAAAAAAAAAAAAAABP#AAAAAAAAAAAAABP#AAAAAAAAD#####AAAAAgAMQ0NvbW1lbnRhaXJlAP####8B#wAAAf####8QQH+4AAAAAABAeyhR64UeuAIAAAAAAAAAAAAAAAABAAAAAAAAAAAABFpPT00AAAAIAP####8AAAAZAAAAAT#weuFHrhR7AAAACwD#####Af8AAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAAkQAAAOAAAAA0AP####8AAAAAAMA0AAAAAAAAwCgAAAAAAAAAAADhEAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAVMAAAATAP####8AAAAaAAAAhQAAABQA#####wEAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAIAAADjAAAAFAD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAQAAAOMAAAAMAP####8AAAAAABAAAAEBAQAAAJAAAADlAAAABgD#####AQAAAAEQAAABAQEAAADQAT#wAAAAAAAAAAAAHgD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAA5wAAAOYAAAAMAP####8Af39#ABAAAAEBAQAAANAAAADoAAAADAD#####AAAAAAAQAAABAQEAAAAZAAAA5QAAAAwA#####wAAAAAAEAAAAQEBAAAAGQAAAJH#####AAAAAgAJQ0NlcmNsZU9SAP####8BAAAAAQEAAADQAAAAAT#ZmZmZmZmaAAAAABMA#####wAAAOkAAADsAAAAFAD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAQAAAO0AAAAUAP####8AAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQACAAAA7QAAABMA#####wAAAOsAAADsAAAAFAD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAgAAAPAAAAAUAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQABAAAA8AAAAAgA#####wAAANAAAAAYBAAAAAoAAAA1AAAACwD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAA8gAAAPMAAAARAP####8AAADQAAAA9AAAAAsA#####wEAAAAAEAAAAEAIAAAAAAAAAAAAAAAAAAAFAAAAAO4AAAD1AAAADAD#####AAAAAAAQAAABAQEAAAD0AAAA0AAAAAwA#####wAAAAAAEAAAAQEBAAAA0AAAAO4AAAAMAP####8AAAAAABAAAAEBAQAAAO4AAAD2AAAADAD#####AAAAAAAQAAABAQEAAAD2AAAA9P####8AAAABAAlDUG9seWdvbmUA#####wAAAAABAQAAAAUAAAD0AAAA0AAAAO4AAAD2AAAA9AAAABEA#####wAAANAAAADuAAAACwD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAAGQAAAPwAAAALAP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAAAZAAAA9QAAABEA#####wAAABkAAAD+AAAACwD#####AQAAAAAQAAAAQAgAAAAAAAAAAAAAAAAAAAUAAAAA#QAAAP8AAAAMAP####8AAAAAABAAAAEBAQAAAP4AAAAZAAAADAD#####AAAAAAAQAAABAQEAAAAZAAAA#QAAAAwA#####wAAAAAAEAAAAQEBAAAA#QAAAQAAAAAMAP####8AAAAAABAAAAEBAQAAAQAAAAD+AAAANgD#####AAAAAAEBAAAABQAAAP4AAAAZAAAA#QAAAQAAAAD+AAAABgD#####AQAAAAEQAAABAQEAAAAQAT#wAAAAAAAAAAAANQD#####AQAAAAEBAAAAEAAAAAE#yZmZmZmZmgAAAAATAP####8AAAEGAAABBwAAABQA#####wEAAAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAEAAAEIAAAAFAD#####AQAAAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAgAAAQgAAAAMAP####8B#wAAABAAAAEAAQAAAQoAAAEJ#####wAAAAEAB0NNaWxpZXUA#####wH#AAAAEAAAAAAAAAAAAAAAQAgAAAAAAAAFAAAAANAAAACQAAAANwD#####Af8AAAAQAAAAAAAAAAAAAABACAAAAAAAAAUAAAAAGQAAANAAAAAOAP####8BAAAAAMAqAAAAAAAAwBwAAAAAAAAAAAEMEAAAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAAAgAAAB0AAAA3AP####8BAAAAABAAAAAAAAAAAAAAAEAIAAAAAAAABQAAAAB5AAAAGQAAAA4A#####wEAAAAAwBwAAAAAAAAAAAAAAAAAAAAAAQ8QAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAAAAAACAAAAHgAAAAQA#####wACaDMABWgxLWgyAAAACQEAAAAKAAAAHAAAAAoAAAAdAAAADgD#####AQAAAADANQAAAAAAAMAiAAAAAAAAAAABDRAAAAAAAAAAAAAAAAAAAQAAAAAAAAAAAAAAAAEAAAERAAAAGP##########'
        if (!context.isHtml) { texte = '\\begin{minipage}{0.7 \\linewidth} \n\t' } else { texte = '' }
        texte += `Un cône de glace d'une marque célèbre a pour rayon $${texNombre(r, 1)}${sp()}$cm et pour hauteur $SO${sp()}=${sp()}${texNombre(h1, 1)}${sp()}$cm.<br>`
        texte += `Le fabricant a coulé au fond de ce cône du chocolat sur une hauteur SO' de ${texNombre(h2, 0)}${sp()}cm.<br>`
        texte += numAlpha(0) + ' Calculer le volume total du cône.<br>'
        texte += numAlpha(1) + ' En déduire le volume de chocolat présent dans le fond du cône.<br>'
        texte += numAlpha(2) + ' Déduire des deux premières questions le volume de glace permettant de remplir le cône.<br>'
        texte += numAlpha(3) + ' Si la glace avait été mise dans le cône avant le chocolat, quelle serait la hauteur atteinte par la glace dans le cône ?<br>'
        texte += numAlpha(4) + ' Quelle serait alors l\'épaisseur de chocolat au dessus de la glace ?<br>'
        if (context.isHtml) { texte += 'Le point O peut être déplacé et on peut changer l\'angle de vue &#x3C6; ' } else {
          texte += `\n\t \\end{minipage} \n\t \\begin{minipage}{0.3 \\linewidth} \n\t \\begin{tikzpicture}[scale=0.8]
          \\definecolor{hhhhhh}{rgb}{0,0,0}
          \\definecolor{phphph}{rgb}{0.5,0.5,0.5}
          \\definecolor{ofofof}{rgb}{0.5,0.5,0.5}
          \\definecolor{ffffhh}{rgb}{1,1,0}
          \\definecolor{enenen}{rgb}{0.9,0.9,0.9}
          \\definecolor{dpdpdp}{rgb}{0.85,0.85,0.85}
          \\definecolor{bdbdbd}{rgb}{0.74,0.74,0.74}
          \\definecolor{alalal}{rgb}{0.64,0.64,0.64}
          \\definecolor{ffhhhh}{rgb}{1,0,0}
          \\clip (40.89,0) rectangle (0,22.58);
          \\fill[color=black] (4.641,21.063) circle (0.063);
          \\node at (4.234, 20.625) [align=left,inner sep = 0pt, outer sep = 0pt,below right,black,font= \\sf \\fontsize {0.438cm} {0.547cm} \\selectfont] {$\\text{O}$};
          \\draw [color=ofofof , dotted, line width = 0.4](7.847,20.165)--(7.675,20.12)--(7.495,20.076)--(7.306,20.036)--(7.111,19.998)--(6.909,19.964)--(6.7,19.932)--(6.486,19.903)--(6.267,19.878)--(6.043,19.856)--(5.816,19.837)--(5.585,19.821)--(5.351,19.809)--(5.116,19.8)--(4.88,19.795)--(4.642,19.793)--(4.405,19.795)--(4.169,19.8)--(3.933,19.809)--(3.7,19.821)--(3.469,19.836)--(3.242,19.855)--(3.018,19.877)--(2.799,19.903)--(2.584,19.931)--(2.376,19.963)--(2.173,19.998)--(1.978,20.035)--(1.789,20.076)--(1.609,20.119)--(1.437,20.165)--(1.273,20.213)--(1.119,20.263)--(0.974,20.316)--(0.84,20.371)--(0.716,20.427)--(0.603,20.486)--(0.5,20.546)--(0.409,20.607)--(0.33,20.67)--(0.263,20.734)--(0.207,20.798)--(0.164,20.863)--(0.133,20.929)--(0.114,20.996)--(0.108,21.062)--(0.114,21.128)--(0.132,21.195)--(0.163,21.261)--(0.206,21.326)--(0.262,21.391)--(0.329,21.454)--(0.408,21.517)--(0.499,21.578)--(0.601,21.638)--(0.714,21.697)--(0.838,21.753)--(0.972,21.808)--(1.117,21.861)--(1.271,21.911)--(1.434,21.96)--(1.606,22.005)--(1.787,22.049)--(1.975,22.089)--(2.17,22.127)--(2.373,22.161)--(2.581,22.193)--(2.795,22.222)--(3.015,22.247)--(3.238,22.269)--(3.466,22.288)--(3.696,22.304)--(3.93,22.316)--(4.165,22.325)--(4.402,22.33)--(4.639,22.332)--(4.876,22.33)--(5.113,22.325)--(5.348,22.316)--(5.581,22.304)--(5.812,22.289)--(6.04,22.27)--(6.263,22.248)--(6.483,22.222)--(6.697,22.194)--(6.906,22.162)--(7.108,22.127)--(7.304,22.09)--(7.492,22.049)--(7.672,22.006)--(7.845,21.96)--(8.008,21.912)--(8.162,21.862)--(8.307,21.809)--(8.441,21.754)--(8.565,21.698)--(8.679,21.639)--(8.781,21.579)--(8.872,21.518)--(8.951,21.455)--(9.019,21.391)--(9.074,21.327)--(9.117,21.262)--(9.149,21.196)--(9.167,21.129)--(9.174,21.063)--(9.167,20.997)--(9.149,20.93)--(9.118,20.864)--(9.075,20.799)--(9.02,20.734)--(8.952,20.671)--(8.873,20.608)--(8.782,20.547)--(8.68,20.487)--(8.567,20.428)--(8.443,20.372)--(8.309,20.317)--(8.164,20.264)--(8.01,20.214)--cycle;
          
          \\fill[color = ffffhh, opacity = 0.2](7.847,20.165)--(7.675,20.12)--(7.495,20.076)--(7.306,20.036)--(7.111,19.998)--(6.909,19.964)--(6.7,19.932)--(6.486,19.903)--(6.267,19.878)--(6.043,19.856)--(5.816,19.837)--(5.585,19.821)--(5.351,19.809)--(5.116,19.8)--(4.88,19.795)--(4.642,19.793)--(4.405,19.795)--(4.169,19.8)--(3.933,19.809)--(3.7,19.821)--(3.469,19.836)--(3.242,19.855)--(3.018,19.877)--(2.799,19.903)--(2.584,19.931)--(2.376,19.963)--(2.173,19.998)--(1.978,20.035)--(1.789,20.076)--(1.609,20.119)--(1.437,20.165)--(1.273,20.213)--(1.119,20.263)--(0.974,20.316)--(0.84,20.371)--(0.716,20.427)--(0.603,20.486)--(0.5,20.546)--(0.409,20.607)--(0.33,20.67)--(0.263,20.734)--(0.207,20.798)--(0.164,20.863)--(0.133,20.929)--(0.114,20.996)--(0.108,21.062)--(0.114,21.128)--(0.132,21.195)--(0.163,21.261)--(0.206,21.326)--(0.262,21.391)--(0.329,21.454)--(0.408,21.517)--(0.499,21.578)--(0.601,21.638)--(0.714,21.697)--(0.838,21.753)--(0.972,21.808)--(1.117,21.861)--(1.271,21.911)--(1.434,21.96)--(1.606,22.005)--(1.787,22.049)--(1.975,22.089)--(2.17,22.127)--(2.373,22.161)--(2.581,22.193)--(2.795,22.222)--(3.015,22.247)--(3.238,22.269)--(3.466,22.288)--(3.696,22.304)--(3.93,22.316)--(4.165,22.325)--(4.402,22.33)--(4.639,22.332)--(4.876,22.33)--(5.113,22.325)--(5.348,22.316)--(5.581,22.304)--(5.812,22.289)--(6.04,22.27)--(6.263,22.248)--(6.483,22.222)--(6.697,22.194)--(6.906,22.162)--(7.108,22.127)--(7.304,22.09)--(7.492,22.049)--(7.672,22.006)--(7.845,21.96)--(8.008,21.912)--(8.162,21.862)--(8.307,21.809)--(8.441,21.754)--(8.565,21.698)--(8.679,21.639)--(8.781,21.579)--(8.872,21.518)--(8.951,21.455)--(9.019,21.391)--(9.074,21.327)--(9.117,21.262)--(9.149,21.196)--(9.167,21.129)--(9.174,21.063)--(9.167,20.997)--(9.149,20.93)--(9.118,20.864)--(9.075,20.799)--(9.02,20.734)--(8.952,20.671)--(8.873,20.608)--(8.782,20.547)--(8.68,20.487)--(8.567,20.428)--(8.443,20.372)--(8.309,20.317)--(8.164,20.264)--(8.01,20.214)(7.847,20.165);
          \\draw [color=black , line width = 0.8](4.641,8.629)--(9.15,20.933);
          \\draw [color=black , line width = 0.8](4.641,8.629)--(0.131,20.933);
          \\draw [color=dpdpdp , line width = 0.4](4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629)--(4.641,8.629);
          
          \\draw [color=dpdpdp , line width = 0.4](4.14,10.025)--(4.138,10.019)--(4.137,10.013)--(4.137,10.007)--(4.138,10.001)--(4.14,9.995)--(4.143,9.99)--(4.146,9.984)--(4.151,9.978)--(4.156,9.972)--(4.163,9.966)--(4.17,9.961)--(4.178,9.955)--(4.187,9.95)--(4.196,9.944)--(4.207,9.939)--(4.218,9.934)--(4.23,9.929)--(4.243,9.924)--(4.256,9.92)--(4.27,9.915)--(4.285,9.911)--(4.301,9.907)--(4.317,9.903)--(4.333,9.899)--(4.35,9.896)--(4.368,9.892)--(4.386,9.889)--(4.405,9.886)--(4.424,9.884)--(4.443,9.881)--(4.463,9.879)--(4.483,9.877)--(4.504,9.875)--(4.524,9.874)--(4.545,9.872)--(4.566,9.871)--(4.587,9.871)--(4.609,9.87)--(4.63,9.87)--(4.651,9.87)--(4.673,9.87)--(4.694,9.871)--(4.715,9.871)--(4.736,9.872)--(4.757,9.874)--(4.778,9.875)--(4.798,9.877)--(4.818,9.879)--(4.838,9.881)--(4.857,9.884)--(4.876,9.886)--(4.895,9.889)--(4.913,9.892)--(4.931,9.896)--(4.948,9.899)--(4.965,9.903)--(4.981,9.907)--(4.996,9.911)--(5.011,9.915)--(5.025,9.92)--(5.038,9.924)--(5.051,9.929)--(5.063,9.934)--(5.074,9.939)--(5.085,9.944)--(5.094,9.95)--(5.103,9.955)--(5.111,9.961)--(5.119,9.966)--(5.125,9.972)--(5.13,9.978)--(5.135,9.984)--(5.138,9.99)--(5.141,9.995)--(5.143,10.001)--(5.144,10.007)--(5.144,10.013)--(5.143,10.019)--(5.142,10.025);
          
          \\draw [color=dpdpdp , line width = 0.4](3.639,11.421)--(3.635,11.409)--(3.633,11.397)--(3.634,11.385)--(3.636,11.373)--(3.639,11.361)--(3.645,11.35)--(3.652,11.338)--(3.661,11.326)--(3.672,11.315)--(3.685,11.303)--(3.699,11.292)--(3.715,11.281)--(3.733,11.27)--(3.752,11.259)--(3.773,11.249)--(3.796,11.239)--(3.82,11.229)--(3.845,11.219)--(3.872,11.21)--(3.9,11.201)--(3.93,11.193)--(3.96,11.184)--(3.993,11.176)--(4.026,11.169)--(4.06,11.162)--(4.096,11.155)--(4.132,11.149)--(4.169,11.143)--(4.207,11.138)--(4.246,11.133)--(4.286,11.128)--(4.326,11.124)--(4.367,11.121)--(4.408,11.118)--(4.45,11.115)--(4.492,11.113)--(4.534,11.112)--(4.577,11.111)--(4.619,11.11)--(4.662,11.11)--(4.705,11.111)--(4.747,11.112)--(4.789,11.113)--(4.831,11.115)--(4.873,11.118)--(4.914,11.121)--(4.955,11.124)--(4.995,11.128)--(5.035,11.133)--(5.074,11.138)--(5.112,11.143)--(5.149,11.149)--(5.186,11.155)--(5.221,11.162)--(5.255,11.169)--(5.289,11.176)--(5.321,11.184)--(5.352,11.193)--(5.381,11.201)--(5.409,11.21)--(5.436,11.219)--(5.462,11.229)--(5.486,11.239)--(5.508,11.249)--(5.529,11.259)--(5.548,11.27)--(5.566,11.281)--(5.582,11.292)--(5.596,11.303)--(5.609,11.315)--(5.62,11.326)--(5.629,11.338)--(5.636,11.35)--(5.642,11.361)--(5.646,11.373)--(5.648,11.385)--(5.648,11.397)--(5.646,11.409)--(5.643,11.421);
          
          \\draw [color=dpdpdp , line width = 0.4](3.138,12.817)--(3.132,12.799)--(3.13,12.781)--(3.13,12.763)--(3.133,12.745)--(3.139,12.728)--(3.147,12.71)--(3.158,12.692)--(3.172,12.675)--(3.188,12.657)--(3.207,12.64)--(3.228,12.623)--(3.252,12.607)--(3.279,12.59)--(3.308,12.574)--(3.339,12.559)--(3.373,12.544)--(3.409,12.529)--(3.447,12.514)--(3.487,12.5)--(3.53,12.487)--(3.574,12.474)--(3.62,12.462)--(3.669,12.45)--(3.718,12.439)--(3.77,12.428)--(3.823,12.418)--(3.878,12.409)--(3.933,12.4)--(3.991,12.392)--(4.049,12.384)--(4.108,12.378)--(4.169,12.372)--(4.23,12.367)--(4.292,12.362)--(4.354,12.358)--(4.417,12.355)--(4.481,12.353)--(4.545,12.352)--(4.609,12.351)--(4.673,12.351)--(4.737,12.352)--(4.8,12.353)--(4.864,12.355)--(4.927,12.358)--(4.989,12.362)--(5.051,12.367)--(5.113,12.372)--(5.173,12.378)--(5.232,12.384)--(5.291,12.392)--(5.348,12.4)--(5.404,12.409)--(5.458,12.418)--(5.511,12.428)--(5.563,12.439)--(5.613,12.45)--(5.661,12.462)--(5.707,12.474)--(5.751,12.487)--(5.794,12.5)--(5.834,12.514)--(5.872,12.529)--(5.908,12.544)--(5.942,12.559)--(5.973,12.574)--(6.002,12.59)--(6.029,12.607)--(6.053,12.623)--(6.074,12.64)--(6.093,12.657)--(6.11,12.675)--(6.123,12.692)--(6.134,12.71)--(6.143,12.728)--(6.148,12.745)--(6.151,12.763)--(6.151,12.781)--(6.149,12.799)--(6.144,12.817);
          
          \\draw [color=dpdpdp , line width = 0.4](2.637,14.213)--(2.63,14.189)--(2.626,14.165)--(2.627,14.141)--(2.631,14.117)--(2.638,14.094)--(2.649,14.07)--(2.664,14.046)--(2.682,14.023)--(2.704,14)--(2.729,13.977)--(2.758,13.955)--(2.79,13.932)--(2.825,13.911)--(2.864,13.889)--(2.906,13.869)--(2.95,13.848)--(2.998,13.828)--(3.049,13.809)--(3.103,13.791)--(3.16,13.773)--(3.219,13.756)--(3.28,13.739)--(3.345,13.723)--(3.411,13.708)--(3.48,13.694)--(3.55,13.681)--(3.623,13.668)--(3.698,13.657)--(3.774,13.646)--(3.852,13.636)--(3.931,13.627)--(4.011,13.619)--(4.093,13.612)--(4.176,13.606)--(4.259,13.601)--(4.343,13.597)--(4.428,13.594)--(4.513,13.592)--(4.598,13.591)--(4.683,13.591)--(4.769,13.592)--(4.854,13.594)--(4.938,13.597)--(5.022,13.601)--(5.106,13.606)--(5.188,13.612)--(5.27,13.619)--(5.35,13.627)--(5.43,13.636)--(5.507,13.646)--(5.584,13.657)--(5.658,13.668)--(5.731,13.681)--(5.802,13.694)--(5.87,13.708)--(5.937,13.723)--(6.001,13.739)--(6.063,13.756)--(6.122,13.773)--(6.178,13.791)--(6.232,13.809)--(6.283,13.828)--(6.331,13.848)--(6.376,13.869)--(6.418,13.889)--(6.456,13.911)--(6.491,13.932)--(6.523,13.955)--(6.552,13.977)--(6.577,14)--(6.599,14.023)--(6.617,14.046)--(6.632,14.07)--(6.643,14.094)--(6.651,14.117)--(6.655,14.141)--(6.655,14.165)--(6.652,14.189)--(6.645,14.213);
          
          \\draw [color=dpdpdp , line width = 0.4](2.136,15.609)--(2.127,15.579)--(2.123,15.549)--(2.123,15.519)--(2.128,15.489)--(2.137,15.46)--(2.151,15.43)--(2.17,15.401)--(2.192,15.371)--(2.22,15.343)--(2.251,15.314)--(2.287,15.286)--(2.327,15.258)--(2.371,15.231)--(2.42,15.204)--(2.472,15.178)--(2.528,15.153)--(2.588,15.128)--(2.651,15.104)--(2.719,15.081)--(2.789,15.059)--(2.863,15.037)--(2.94,15.017)--(3.02,14.997)--(3.104,14.978)--(3.189,14.96)--(3.278,14.944)--(3.369,14.928)--(3.462,14.914)--(3.557,14.9)--(3.654,14.888)--(3.753,14.877)--(3.854,14.867)--(3.956,14.858)--(4.059,14.851)--(4.164,14.844)--(4.269,14.839)--(4.374,14.836)--(4.481,14.833)--(4.587,14.832)--(4.694,14.832)--(4.801,14.833)--(4.907,14.836)--(5.013,14.839)--(5.118,14.844)--(5.222,14.851)--(5.325,14.858)--(5.427,14.867)--(5.528,14.877)--(5.627,14.888)--(5.724,14.9)--(5.819,14.914)--(5.912,14.928)--(6.003,14.944)--(6.092,14.96)--(6.178,14.978)--(6.261,14.997)--(6.341,15.017)--(6.418,15.037)--(6.492,15.059)--(6.563,15.081)--(6.63,15.104)--(6.693,15.128)--(6.753,15.153)--(6.809,15.178)--(6.862,15.204)--(6.91,15.231)--(6.954,15.258)--(6.994,15.286)--(7.03,15.314)--(7.062,15.343)--(7.089,15.371)--(7.112,15.401)--(7.13,15.43)--(7.144,15.46)--(7.153,15.489)--(7.158,15.519)--(7.159,15.549)--(7.154,15.579)--(7.146,15.609);
          
          \\draw [color=dpdpdp , line width = 0.4](1.634,17.005)--(1.624,16.969)--(1.619,16.933)--(1.62,16.897)--(1.626,16.861)--(1.637,16.826)--(1.653,16.79)--(1.676,16.755)--(1.703,16.72)--(1.735,16.685)--(1.773,16.651)--(1.816,16.617)--(1.864,16.584)--(1.917,16.551)--(1.975,16.519)--(2.038,16.488)--(2.105,16.458)--(2.177,16.428)--(2.254,16.399)--(2.334,16.371)--(2.419,16.345)--(2.508,16.319)--(2.6,16.294)--(2.696,16.27)--(2.796,16.248)--(2.899,16.227)--(3.005,16.207)--(3.114,16.188)--(3.226,16.17)--(3.341,16.154)--(3.457,16.14)--(3.576,16.126)--(3.697,16.114)--(3.819,16.104)--(3.943,16.095)--(4.068,16.087)--(4.194,16.081)--(4.321,16.077)--(4.449,16.074)--(4.577,16.072)--(4.705,16.072)--(4.832,16.074)--(4.96,16.077)--(5.087,16.081)--(5.213,16.087)--(5.338,16.095)--(5.462,16.104)--(5.585,16.114)--(5.705,16.126)--(5.824,16.14)--(5.941,16.154)--(6.055,16.17)--(6.167,16.188)--(6.276,16.207)--(6.382,16.227)--(6.485,16.248)--(6.585,16.27)--(6.681,16.294)--(6.774,16.319)--(6.862,16.345)--(6.947,16.371)--(7.028,16.399)--(7.104,16.428)--(7.176,16.458)--(7.243,16.488)--(7.306,16.519)--(7.364,16.551)--(7.417,16.584)--(7.465,16.617)--(7.508,16.651)--(7.546,16.685)--(7.578,16.72)--(7.606,16.755)--(7.628,16.79)--(7.644,16.826)--(7.656,16.861)--(7.662,16.897)--(7.662,16.933)--(7.657,16.969)--(7.647,17.005);
          
          \\draw [color=dpdpdp , line width = 0.4](1.133,18.4)--(1.121,18.359)--(1.116,18.317)--(1.116,18.275)--(1.123,18.233)--(1.136,18.192)--(1.156,18.15)--(1.181,18.109)--(1.213,18.068)--(1.251,18.028)--(1.295,17.988)--(1.346,17.948)--(1.402,17.91)--(1.464,17.872)--(1.531,17.834)--(1.604,17.798)--(1.683,17.762)--(1.767,17.728)--(1.856,17.694)--(1.95,17.662)--(2.049,17.63)--(2.152,17.6)--(2.26,17.571)--(2.372,17.544)--(2.489,17.518)--(2.609,17.493)--(2.733,17.469)--(2.86,17.448)--(2.99,17.427)--(3.124,17.408)--(3.26,17.391)--(3.399,17.376)--(3.539,17.362)--(3.682,17.35)--(3.827,17.339)--(3.973,17.33)--(4.12,17.323)--(4.268,17.318)--(4.417,17.314)--(4.566,17.313)--(4.715,17.313)--(4.864,17.314)--(5.013,17.318)--(5.161,17.323)--(5.309,17.33)--(5.455,17.339)--(5.599,17.35)--(5.742,17.362)--(5.883,17.376)--(6.021,17.391)--(6.157,17.408)--(6.291,17.427)--(6.421,17.448)--(6.548,17.469)--(6.672,17.493)--(6.793,17.518)--(6.909,17.544)--(7.021,17.571)--(7.129,17.6)--(7.233,17.63)--(7.331,17.662)--(7.425,17.694)--(7.515,17.728)--(7.598,17.762)--(7.677,17.798)--(7.75,17.834)--(7.818,17.872)--(7.88,17.91)--(7.936,17.948)--(7.986,17.988)--(8.03,18.028)--(8.068,18.068)--(8.1,18.109)--(8.126,18.15)--(8.145,18.192)--(8.158,18.233)--(8.165,18.275)--(8.166,18.317)--(8.16,18.359)--(8.148,18.4);
          
          \\draw [color=dpdpdp , line width = 0.4](0.632,19.796)--(0.619,19.749)--(0.612,19.701)--(0.613,19.653)--(0.62,19.605)--(0.636,19.558)--(0.658,19.51)--(0.687,19.463)--(0.724,19.417)--(0.767,19.37)--(0.818,19.325)--(0.875,19.28)--(0.939,19.235)--(1.01,19.192)--(1.087,19.149)--(1.17,19.108)--(1.26,19.067)--(1.356,19.028)--(1.458,18.989)--(1.565,18.952)--(1.678,18.916)--(1.797,18.882)--(1.92,18.849)--(2.048,18.817)--(2.181,18.787)--(2.319,18.759)--(2.46,18.732)--(2.606,18.707)--(2.755,18.684)--(2.907,18.663)--(3.063,18.643)--(3.221,18.625)--(3.382,18.609)--(3.545,18.595)--(3.71,18.583)--(3.877,18.573)--(4.045,18.565)--(4.215,18.559)--(4.385,18.555)--(4.555,18.553)--(4.726,18.553)--(4.896,18.555)--(5.066,18.559)--(5.236,18.565)--(5.404,18.573)--(5.571,18.583)--(5.736,18.595)--(5.899,18.609)--(6.06,18.625)--(6.219,18.643)--(6.374,18.663)--(6.527,18.684)--(6.676,18.707)--(6.821,18.732)--(6.963,18.759)--(7.1,18.787)--(7.233,18.817)--(7.361,18.849)--(7.485,18.882)--(7.603,18.916)--(7.716,18.952)--(7.823,18.989)--(7.925,19.028)--(8.021,19.067)--(8.111,19.108)--(8.194,19.149)--(8.272,19.192)--(8.342,19.235)--(8.406,19.28)--(8.464,19.325)--(8.514,19.37)--(8.558,19.417)--(8.594,19.463)--(8.623,19.51)--(8.646,19.558)--(8.661,19.605)--(8.669,19.653)--(8.669,19.701)--(8.663,19.749)--(8.649,19.796);
          
          \\draw [color=dpdpdp , line width = 0.4](0.131,21.192)--(0.116,21.138)--(0.108,21.085)--(0.109,21.031)--(0.118,20.977)--(0.135,20.924)--(0.16,20.87)--(0.193,20.818)--(0.234,20.765)--(0.283,20.713)--(0.34,20.662)--(0.404,20.611)--(0.476,20.561)--(0.556,20.512)--(0.643,20.464)--(0.737,20.418)--(0.838,20.372)--(0.946,20.327)--(1.06,20.284)--(1.181,20.242)--(1.308,20.202)--(1.441,20.163)--(1.58,20.126)--(1.724,20.091)--(1.874,20.057)--(2.028,20.025)--(2.188,19.995)--(2.351,19.967)--(2.519,19.941)--(2.69,19.917)--(2.865,19.895)--(3.044,19.875)--(3.225,19.857)--(3.408,19.841)--(3.594,19.828)--(3.782,19.816)--(3.971,19.807)--(4.162,19.8)--(4.353,19.796)--(4.545,19.794)--(4.737,19.794)--(4.928,19.796)--(5.12,19.8)--(5.31,19.807)--(5.499,19.816)--(5.687,19.828)--(5.873,19.841)--(6.056,19.857)--(6.238,19.875)--(6.416,19.895)--(6.591,19.917)--(6.762,19.941)--(6.93,19.967)--(7.094,19.995)--(7.253,20.025)--(7.407,20.057)--(7.557,20.091)--(7.701,20.126)--(7.84,20.163)--(7.973,20.202)--(8.1,20.242)--(8.221,20.284)--(8.336,20.327)--(8.444,20.372)--(8.545,20.418)--(8.639,20.464)--(8.725,20.512)--(8.805,20.561)--(8.877,20.611)--(8.942,20.662)--(8.998,20.713)--(9.047,20.765)--(9.088,20.818)--(9.121,20.87)--(9.146,20.924)--(9.163,20.977)--(9.172,21.031)--(9.173,21.085)--(9.165,21.138)--(9.15,21.192);
          
          \\draw [color=black , line width = 0.8](0.131,21.192)--(0.12,21.157)--(0.113,21.121)--(0.108,21.085)--(0.108,21.05)--(0.111,21.014)--(0.118,20.978)--(0.128,20.943)--(0.142,20.907)--(0.159,20.872)--(0.18,20.837)--(0.205,20.802)--(0.232,20.767)--(0.264,20.732)--(0.299,20.698)--(0.337,20.664)--(0.379,20.63)--(0.424,20.597)--(0.472,20.564)--(0.524,20.531)--(0.579,20.499)--(0.637,20.467)--(0.699,20.436)--(0.763,20.405)--(0.831,20.375)--(0.901,20.345)--(0.975,20.316)--(1.051,20.287)--(1.13,20.259)--(1.212,20.232)--(1.297,20.205)--(1.385,20.179)--(1.475,20.154)--(1.567,20.13)--(1.662,20.106)--(1.759,20.083)--(1.859,20.06)--(1.96,20.039)--(2.064,20.018)--(2.17,19.998)--(2.278,19.979)--(2.388,19.961)--(2.499,19.944)--(2.612,19.927)--(2.727,19.912)--(2.843,19.897)--(2.961,19.884)--(3.08,19.871)--(3.2,19.859)--(3.322,19.848)--(3.444,19.838)--(3.568,19.829)--(3.692,19.821)--(3.817,19.814)--(3.942,19.808)--(4.069,19.803)--(4.195,19.799)--(4.322,19.796)--(4.449,19.794)--(4.577,19.793)--(4.704,19.793)--(4.832,19.794)--(4.959,19.796)--(5.086,19.799)--(5.213,19.803)--(5.339,19.808)--(5.465,19.814)--(5.589,19.821)--(5.714,19.829)--(5.837,19.838)--(5.96,19.848)--(6.081,19.859)--(6.201,19.871)--(6.32,19.884)--(6.438,19.897)--(6.554,19.912)--(6.669,19.927)--(6.782,19.944)--(6.894,19.961)--(7.003,19.979)--(7.111,19.998)--(7.217,20.018)--(7.321,20.039)--(7.423,20.06)--(7.522,20.083)--(7.619,20.106)--(7.714,20.13)--(7.807,20.154)--(7.897,20.179)--(7.984,20.205)--(8.069,20.232)--(8.151,20.259)--(8.23,20.287)--(8.306,20.316)--(8.38,20.345)--(8.451,20.375)--(8.518,20.405)--(8.583,20.436)--(8.644,20.467)--(8.702,20.499)--(8.757,20.531)--(8.809,20.564)--(8.857,20.597)--(8.902,20.63)--(8.944,20.664)--(8.982,20.698)--(9.017,20.732)--(9.049,20.767)--(9.077,20.802)--(9.101,20.837)--(9.122,20.872)--(9.139,20.907)--(9.153,20.943)--(9.164,20.978)--(9.17,21.014)--(9.173,21.05)--(9.173,21.085)--(9.169,21.121)--(9.161,21.157)--(9.15,21.192);
          
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(7.847,20.165);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(6.909,19.964);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(5.816,19.837);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(4.642,19.793);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(3.469,19.836);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(2.376,19.963);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(1.437,20.165);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(0.716,20.427);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(0.263,20.734);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(0.108,21.062);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(0.262,21.391);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(0.714,21.697);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(1.434,21.96);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(2.373,22.161);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(3.466,22.288);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(4.639,22.332);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(5.812,22.289);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(6.906,22.162);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(7.845,21.96);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(8.565,21.698);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(9.019,21.391);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(9.174,21.063);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(9.02,20.734);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(8.567,20.428);
          \\draw [color=bdbdbd , dotted, line width = 0.4](4.641,8.629)--(7.847,20.165);
          \\fill[color=black] (4.641,13.603) circle (0.063);
          \\node at (3.641, 13.884) [align=left,inner sep = 0pt, outer sep = 0pt,below right,black,font= \\sf \\fontsize {0.469cm} {0.586cm} \\selectfont] {$\\text{O'}$};
          \\draw [color=enenen , line width = 0.4](4.641,8.629)--(5.051,20.948);
          \\draw [color=enenen , line width = 0.4](7.818,21.953)--(4.641,8.629);
          \\draw [color=alalal , dotted, line width = 0.4](6.424,13.512)--(6.405,13.486)--(6.381,13.46)--(6.352,13.435)--(6.319,13.411)--(6.281,13.386)--(6.239,13.363)--(6.192,13.34)--(6.142,13.318)--(6.087,13.296)--(6.028,13.276)--(5.966,13.256)--(5.899,13.237)--(5.83,13.219)--(5.757,13.203)--(5.682,13.187)--(5.603,13.172)--(5.522,13.159)--(5.439,13.147)--(5.353,13.136)--(5.266,13.126)--(5.177,13.118)--(5.086,13.111)--(4.994,13.105)--(4.901,13.1)--(4.808,13.097)--(4.714,13.095)--(4.62,13.095)--(4.526,13.096)--(4.432,13.098)--(4.339,13.102)--(4.246,13.107)--(4.155,13.114)--(4.065,13.121)--(3.977,13.13)--(3.89,13.141)--(3.805,13.152)--(3.723,13.165)--(3.643,13.179)--(3.566,13.194)--(3.491,13.21)--(3.42,13.227)--(3.352,13.245)--(3.288,13.265)--(3.227,13.285)--(3.17,13.306)--(3.117,13.328)--(3.068,13.35)--(3.023,13.373)--(2.983,13.397)--(2.947,13.421)--(2.916,13.446)--(2.889,13.472)--(2.867,13.497)--(2.85,13.523)--(2.838,13.549)--(2.83,13.576)--(2.827,13.602)--(2.83,13.628)--(2.837,13.655)--(2.849,13.681)--(2.866,13.707)--(2.888,13.732)--(2.914,13.758)--(2.945,13.782)--(2.981,13.807)--(3.021,13.831)--(3.065,13.854)--(3.114,13.876)--(3.167,13.898)--(3.223,13.919)--(3.284,13.939)--(3.348,13.959)--(3.416,13.977)--(3.487,13.994)--(3.561,14.011)--(3.638,14.026)--(3.718,14.04)--(3.8,14.053)--(3.885,14.064)--(3.972,14.074)--(4.06,14.084)--(4.15,14.091)--(4.241,14.098)--(4.333,14.103)--(4.427,14.107)--(4.52,14.109)--(4.614,14.11)--(4.709,14.11)--(4.802,14.108)--(4.896,14.105)--(4.989,14.101)--(5.081,14.095)--(5.171,14.088)--(5.261,14.08)--(5.348,14.07)--(5.434,14.059)--(5.518,14.047)--(5.599,14.034)--(5.677,14.019)--(5.753,14.004)--(5.826,13.987)--(5.896,13.969)--(5.962,13.95)--(6.024,13.931)--(6.083,13.91)--(6.138,13.889)--(6.189,13.867)--(6.236,13.844)--(6.279,13.82)--(6.317,13.796)--(6.351,13.771)--(6.38,13.746)--(6.404,13.721)--(6.423,13.695)--(6.438,13.669)--(6.448,13.643)--(6.453,13.617)--(6.453,13.59)--(6.448,13.564)--cycle;
          
          \\fill[color = ffhhhh, opacity = 0.2](6.424,13.512)--(6.405,13.486)--(6.381,13.46)--(6.352,13.435)--(6.319,13.411)--(6.281,13.386)--(6.239,13.363)--(6.192,13.34)--(6.142,13.318)--(6.087,13.296)--(6.028,13.276)--(5.966,13.256)--(5.899,13.237)--(5.83,13.219)--(5.757,13.203)--(5.682,13.187)--(5.603,13.172)--(5.522,13.159)--(5.439,13.147)--(5.353,13.136)--(5.266,13.126)--(5.177,13.118)--(5.086,13.111)--(4.994,13.105)--(4.901,13.1)--(4.808,13.097)--(4.714,13.095)--(4.62,13.095)--(4.526,13.096)--(4.432,13.098)--(4.339,13.102)--(4.246,13.107)--(4.155,13.114)--(4.065,13.121)--(3.977,13.13)--(3.89,13.141)--(3.805,13.152)--(3.723,13.165)--(3.643,13.179)--(3.566,13.194)--(3.491,13.21)--(3.42,13.227)--(3.352,13.245)--(3.288,13.265)--(3.227,13.285)--(3.17,13.306)--(3.117,13.328)--(3.068,13.35)--(3.023,13.373)--(2.983,13.397)--(2.947,13.421)--(2.916,13.446)--(2.889,13.472)--(2.867,13.497)--(2.85,13.523)--(2.838,13.549)--(2.83,13.576)--(2.827,13.602)--(2.83,13.628)--(2.837,13.655)--(2.849,13.681)--(2.866,13.707)--(2.888,13.732)--(2.914,13.758)--(2.945,13.782)--(2.981,13.807)--(3.021,13.831)--(3.065,13.854)--(3.114,13.876)--(3.167,13.898)--(3.223,13.919)--(3.284,13.939)--(3.348,13.959)--(3.416,13.977)--(3.487,13.994)--(3.561,14.011)--(3.638,14.026)--(3.718,14.04)--(3.8,14.053)--(3.885,14.064)--(3.972,14.074)--(4.06,14.084)--(4.15,14.091)--(4.241,14.098)--(4.333,14.103)--(4.427,14.107)--(4.52,14.109)--(4.614,14.11)--(4.709,14.11)--(4.802,14.108)--(4.896,14.105)--(4.989,14.101)--(5.081,14.095)--(5.171,14.088)--(5.261,14.08)--(5.348,14.07)--(5.434,14.059)--(5.518,14.047)--(5.599,14.034)--(5.677,14.019)--(5.753,14.004)--(5.826,13.987)--(5.896,13.969)--(5.962,13.95)--(6.024,13.931)--(6.083,13.91)--(6.138,13.889)--(6.189,13.867)--(6.236,13.844)--(6.279,13.82)--(6.317,13.796)--(6.351,13.771)--(6.38,13.746)--(6.404,13.721)--(6.423,13.695)--(6.438,13.669)--(6.448,13.643)--(6.453,13.617)--(6.453,13.59)--(6.448,13.564)(6.424,13.512);
          \\node at (3.953, 8.694) [align=left,below right ,black,,font= \\sf \\fontsize {0.469cm} {0.586cm} \\selectfont] {S};
          \\draw [color=black , dotted, line width = 0.4](4.641,8.629)--(9.174,21.063);
          \\draw [color=ofofof , dotted, line width = 0.4](4.641,13.603)--(6.454,13.603);
          \\draw [color=black , dotted, line width = 0.4](4.641,21.063)--(9.174,21.063);
          \\draw [color=black , dotted, line width = 0.4](4.641,21.063)--(4.641,8.629);
          \\draw [color=black , dotted, line width = 0.4](4.641,13.987)--(4.641,13.603);
          \\draw [color=black , dotted, line width = 0.4](4.641,13.603)--(5.041,13.603);
          \\draw [color=black , dotted, line width = 0.4](5.041,13.603)--(5.041,13.987);
          \\draw [color=black , dotted, line width = 0.4](5.041,13.987)--(4.641,13.987);
          \\draw [color=black , dotted, line width = 0.4](4.641,13.987)--(4.641,13.603)--(5.041,13.603)--(5.041,13.987)--(4.641,13.987)--cycle;
          \\draw [color=black , dotted, line width = 0.4](4.641,21.447)--(4.641,21.063);
          \\draw [color=black , dotted, line width = 0.4](4.641,21.063)--(5.041,21.063);
          \\draw [color=black , dotted, line width = 0.4](5.041,21.063)--(5.041,21.447);
          \\draw [color=black , dotted, line width = 0.4](5.041,21.447)--(4.641,21.447);
          \\draw [color=black , dotted, line width = 0.4](4.641,21.447)--(4.641,21.063)--(5.041,21.063)--(5.041,21.447)--(4.641,21.447)--cycle;
          \\end{tikzpicture} \n\t \\end{minipage}`
        }
        texteCorr = numAlpha(0) + ` Le volume du cône est $\\dfrac{A_\\text{base}}{3}\\times \\text{hauteur}$ cm${texteExposant(3)} $= \\dfrac{${texNombre(r.pow(2), 2)}\\pi}{3} \\times ${texNombre(h1, 1)}$ cm${texteExposant(3)} $= \\dfrac{${texNombre(r.mul(r).mul(h1), 3)}}{3}\\pi$ cm${texteExposant(3)} $\\approx ${texNombre(r.mul(r).mul(h1).mul(pi).div(3), 3)}$ cm${texteExposant(3)}.<br>`
        texteCorr += numAlpha(1) + ` Le cône de chocolat est une réduction du cône complet. Le coefficient de réduction est $\\dfrac{${texNombre(h2, 1)}}{${texNombre(h1, 1)}}`
        if (!Number.isInteger(h1) || pgcd(h2, h1) > 1) { texteCorr += `=${texFractionReduite(h2.mul(10), h1.mul(10))}$.<br>` } else { texteCorr += '.$<br>' }
        texteCorr += ` Dans une réduction de coefficient k, les volumes sont multipliés par k${texteExposant(3)}.<br>`
        texteCorr += `Donc le volume du cône de hauteur SO' est : $\\left(${texFractionReduite(h2.mul(10), h1.mul(10))}\\right)^3 \\times \\dfrac{${texNombre(r.mul(r).mul(h1), 3)}}{3}\\pi$ cm${texteExposant(3)} $ \\approx ${texNombre(pi.mul(h2.pow(3)).mul(r.pow(2)).div(h1.pow(2)).div(3), 3)}$ cm${texteExposant(3)}.<br>`
        texteCorr += numAlpha(2) + ' Le volume de glace est la différence entre les deux volumes précédents :<br>'
        texteCorr += `$${texNombre(r.pow(2).mul(h1).mul(pi).div(3), 3)}$ cm${texteExposant(3)}$ - ${texNombre(pi.mul(h2.pow(3)).mul(r.div(h1).pow(2)).div(3), 3)}$ cm${texteExposant(3)} $ \\approx ${texNombre(pi.div(3).mul(r.pow(2)).mul(h1.sub(h2.pow(3).div(h1.pow(2)))), 2)}$ cm${texteExposant(3)}.<br>`
        texteCorr += numAlpha(3) + ' Si on verse la glace au fond du cône, on obtient une nouvelle réduction du cône complet.<br>'
        texteCorr += `Soit k' le coefficient de cette réduction, on a : k'${texteExposant(3)} $= 1- \\text{k}^3$`
        texteCorr += ', d\'où k\' '
        texteCorr += '$= \\sqrt[3]{1-{\\text{k}^3}}$.<br>'
        kprime = new Decimal(1).sub(h2.div(h1).pow(3)).cbrt()
        texteCorr += `Donc k' = $\\sqrt[3]{1 - \\left(${texFractionReduite(h2.mul(10), h1.mul(10))}\\right)^3} \\approx ${texNombre(kprime, 5)}$.<br>`
        texteCorr += `On en déduit que la hauteur de glace est approximativement : $${texNombre(kprime, 5)} \\times ${texNombre(h1, 1)}$ cm $\\approx ${texNombre(kprime.mul(h1), 4)}$ cm.<br>`
        texteCorr += numAlpha(4) + ` L'épaisseur de chocolat est alors de : $${texNombre(h1, 1)}\\text{ cm}-${texNombre(kprime.mul(h1), 4)} \\text{ cm}\\approx ${texNombre(h1.sub(kprime.mul(h1)).mul(10), 2)}$ mm !`
        this.MG32codeBase64 = codeBase64
        this.mg32init = (mtg32App, idDoc) => {
          mtg32App.giveFormula2(idDoc, 'r', r.toString())
          mtg32App.giveFormula2(idDoc, 'h1', h1.toString())
          mtg32App.giveFormula2(idDoc, 'h2', h2.toString())
          mtg32App.calculate(idDoc, true)
          return mtg32App.display(idDoc)
        }
        break
    }

    this.listeQuestions.push(texte)
    this.listeCorrections.push(texteCorr)
    listeQuestionsToContenu(this)
  }
  this.besoinFormulaireNumerique = ['Type d\'exercices', 3, ' 1 : Calcul d\' aire et de volumes\n 2 : Problème complexe\n 3 : Mélange']
  this.besoinFormulaire2Numerique = ['Coefficient de réduction (problèmes de type 1)', 3, ' 1 : Décimal\n 2 : Non décimal\n 3 : Mélange']
}