{"version":3,"file":"3G44-_mHDoKgQ.js","sources":["../../src/exercices/3e/3G44.js"],"sourcesContent":["import { tracePoint } from '../../lib/2d/points.js'\nimport { longueur, segment } from '../../lib/2d/segmentsVecteurs.js'\nimport { labelPoint } from '../../lib/2d/textes.js'\nimport { choice, shuffle } from '../../lib/outils/arrayOutils'\nimport { miseEnEvidence, texteEnCouleurEtGras } from '../../lib/outils/embellissements'\nimport { choisitLettresDifferentes } from '../../lib/outils/aleatoires'\nimport { arrondi, nombreDeChiffresDe, rangeMinMax } from '../../lib/outils/nombres.js'\nimport { sp } from '../../lib/outils/outilString.js'\nimport { texNombre } from '../../lib/outils/texNombre.js'\nimport Exercice from '../Exercice.js'\nimport { context } from '../../modules/context.js'\nimport { calculANePlusJamaisUtiliser, gestionnaireFormulaireTexte, listeQuestionsToContenu, randint } from '../../modules/outils.js'\nimport Grandeur from '../../modules/Grandeur'\nimport {\n  CodageAngleDroit3D,\n  cone3d,\n  cube3d,\n  cylindre3d,\n  droite3d,\n  pave3d,\n  point3d,\n  polygone3d,\n  pyramide3d,\n  rotation3d,\n  sphere3d,\n  translation3d,\n  vecteur3d\n} from '../../modules/3d.js'\nimport { assombrirOuEclaircir, colorToLatexOrHTML, fixeBordures, mathalea2d } from '../../modules/2dGeneralites.js'\nimport { ajouteChampTexteMathLive } from '../../lib/interactif/questionMathLive.js'\nimport { RedactionPythagore } from '../4e/_pythagore.js'\nimport { setReponse } from '../../lib/interactif/gestionInteractif.js'\n\nexport const titre = 'Determining lengths in geometry in space'\nexport const amcReady = true\nexport const amcType = 'AMCHybride'\nexport const interactifReady = true\nexport const interactifType = 'mathLive'\nexport const dateDePublication = '19/12/2022'\nexport const dateDeModifImportante = '13/11/2023'\n\n/**\n * Calcul de longueurs avec Pythagore dans la géométrie dans l'espace\n * @author Eric Elter\n */\n\nexport const uuid = '57c70'\nexport const ref = '3G44'\nexport default function CalculPythagoreEspace () {\n  Exercice.call(this) // Héritage de la classe Exercice()\n  this.titre = titre\n  this.nbQuestions = 4\n  this.sup2 = 1\n  this.sup = 10\n\n  this.nouvelleVersion = function () {\n    this.autoCorrection = []\n\n    const listeTypeDeQuestions = gestionnaireFormulaireTexte({\n      saisie: this.sup,\n      min: 1,\n      max: 9,\n      defaut: 10,\n      melange: 10,\n      nbQuestions: this.nbQuestions\n    }) // Tous les types de questions sont posées mais l'ordre diffère à chaque 'cycle'\n    this.listeQuestions = [] // Liste de questions\n    this.listeCorrections = [] // Liste de questions corrigées\n    const listeUnites = [\n      'km',\n      'hmm',\n      'dam',\n      'm',\n      'dm',\n      'cm',\n      'mm'\n    ]\n    for (let i = 0, texte, texteCorr, reponse, objetsEnonce, A, B, C, D, E, BC, segmentATrouver, segmentAnnexe, solideDessine, longueurATrouver, nomSolide, segmentChoisi, choixSegments = [],\n      L, p, J, K, M, JK, I, choixProfondeur, h, c, j, anglesPossibles, indiceAngleChoisi, ptBase, ptBase2, ptsBase, nbSommets, numeroSommet,\n      r, r2, v, sph, cpt = 0; i < this.nbQuestions && cpt < 50;) {\n      this.autoCorrection[i] = {}\n      texte = ''\n      texteCorr = ''\n      objetsEnonce = []\n      context.anglePerspective = choice([-30, -60, 30, 60])\n      j = randint(0, 6) // Permet de choisir l'unité utilisée dans chaque question\n      switch (listeTypeDeQuestions[i]) {\n        case 1: // Diagonale de la face d'un cube\n          A = point3d(0, 0, 0)\n          c = randint(5, 10)\n          B = point3d(c, 0, 0)\n          D = point3d(0, 0, c)\n          choixProfondeur = choice([c, -c])\n          E = point3d(0, choixProfondeur, 0)\n\n          nomSolide = choisitLettresDifferentes(8, 'OQWX').join('')\n          solideDessine = pave3d(A, B, D, E, 'blue', true, nomSolide)\n\n          choixSegments.push(['02', '1'], ['13', '2'])\n          if (choixProfondeur > 0) {\n            choixSegments.push(['16', '5'], ['25', '6']) // Ce sont les diagonales des faces visibles et le sommet qui forme un triangle rectangle\n            if (context.anglePerspective > 0) choixSegments.push(['27', '3'], ['36', '2'])\n            else choixSegments.push(['14', '5'], ['05', '1'])\n          } else {\n            choixSegments.push(['07', '3'], ['34', '0']) // Ce sont les diagonales des faces visibles et le sommet qui forme un triangle rectangle\n            if (context.anglePerspective < 0) choixSegments.push(['27', '3'], ['36', '2'])\n            else choixSegments.push(['14', '5'], ['05', '1'])\n          }\n          segmentChoisi = choice(choixSegments)\n          J = nomSolide[parseInt(segmentChoisi[0][0])]\n          K = nomSolide[parseInt(segmentChoisi[0][1])]\n          I = nomSolide[parseInt(segmentChoisi[1])] // IJK est rectangle en I\n          longueurATrouver = J + K\n          texte += `Knowing that the cube $${nomSolide}$ has edges of $${c}$ ${listeUnites[j]}, calculate the length $${longueurATrouver}$, rounded to the tenth of ${listeUnites[j]}.<br>`\n          segmentATrouver = segment(solideDessine.sommets[parseInt(segmentChoisi[0][0])].c2d, solideDessine.sommets[parseInt(segmentChoisi[0][1])].c2d, '#f15929')\n          segmentATrouver.epaisseur = 2\n          objetsEnonce.push(...solideDessine.c2d, segmentATrouver)\n          texte += mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), {\n            scale: 0.7,\n            style: 'block'\n          }), objetsEnonce) + '<br>'\n          objetsEnonce.push(new CodageAngleDroit3D(solideDessine.sommets[parseInt(segmentChoisi[0][0])], solideDessine.sommets[parseInt(segmentChoisi[1])], solideDessine.sommets[parseInt(segmentChoisi[0][1])], '#f15929', 2))\n          texteCorr += '<br>' + mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), {\n            scale: 0.7,\n            style: 'block'\n          }), objetsEnonce) + '<br>'\n          reponse = arrondi(Math.sqrt(c ** 2 + c ** 2), 1)\n          texteCorr += '<br>' + RedactionPythagore(I, J, K, 1, c, c, reponse, listeUnites[j])[0]\n\n          break\n        case 2: // Diagonale d'un cube\n          // c = new Decimal(randint(2, 10)).plus(Decimalpart1)\n          c = randint(5, 10)\n          nomSolide = choisitLettresDifferentes(8, 'OQWX')\n          nomSolide = nomSolide.join('')\n          choixSegments = [['60', '5', '05', '1'], ['71', '4', '14', '0'], ['24', '1', '41', '0'], ['35', '0', '50', '1']] // Ce sont les diagonales du cubes, le sommet qui forme un triangle rectangle, la diagonale d'une face et le sommet qui forme un triangle rectangle avec cette dernière diagonale\n          segmentChoisi = choice(choixSegments)\n          B = nomSolide[parseInt(segmentChoisi[0][0])]\n          C = nomSolide[parseInt(segmentChoisi[0][1])]\n          A = nomSolide[parseInt(segmentChoisi[1])] // ABC est rectangle en A\n          D = nomSolide[parseInt(segmentChoisi[3])] // ACD est rectangle en D\n\n          longueurATrouver = B + C\n          texte += `Knowing that the cube $${nomSolide}$ has edges of $${c}$ ${listeUnites[j]}, calculate the length $${longueurATrouver}$, rounded to the tenth of ${listeUnites[j]}.<br>`\n          solideDessine = cube3d(1, 1, 1, c, 'blue', '', '', '', false, true, nomSolide)\n          segmentATrouver = segment(solideDessine.sommets[parseInt(segmentChoisi[0][0])].c2d, solideDessine.sommets[parseInt(segmentChoisi[0][1])].c2d, '#f15929')\n          segmentATrouver.epaisseur = 2\n          segmentATrouver.pointilles = 2\n          objetsEnonce.push(...solideDessine.c2d, segmentATrouver)\n          texte += mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), {\n            scale: 0.7,\n            style: 'block'\n          }), objetsEnonce) + '<br>'\n          objetsEnonce.push(new CodageAngleDroit3D(solideDessine.sommets[parseInt(segmentChoisi[0][0])], solideDessine.sommets[parseInt(segmentChoisi[1])], solideDessine.sommets[parseInt(segmentChoisi[0][1])], '#f15929', 2))\n          segmentAnnexe = segment(solideDessine.sommets[parseInt(segmentChoisi[1])].c2d, solideDessine.sommets[parseInt(segmentChoisi[0][1])].c2d, 'green')\n          segmentAnnexe.epaisseur = 2\n          segmentAnnexe.pointilles = 1\n          objetsEnonce.push(segmentAnnexe)\n          objetsEnonce.push(new CodageAngleDroit3D(solideDessine.sommets[parseInt(segmentChoisi[1])], solideDessine.sommets[parseInt(segmentChoisi[3])], solideDessine.sommets[parseInt(segmentChoisi[0][1])], 'green', 2))\n          texteCorr += '<br>' + mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), {\n            scale: 0.7,\n            style: 'block'\n          }), objetsEnonce) + '<br>'\n          texteCorr += `The triangle $${longueurATrouver + A}$ is right-angled in $${A}$ so according to the Pythagorean theorem, we have:`\n          texteCorr += `$${longueurATrouver}^2=${A + B}^2+${A + C}^2$.`\n          texteCorr += `<br> We cannot continue if we do not know the value of $${A + C}^2$. Let's find it.`\n          texteCorr += `<br> ${sp(10)}The triangle $${C + A + D}$ is right-angled in $${D}$ so according to the Pythagorean theorem, we have:`\n          texteCorr += `$${A + C}^2=${A + D}^2+${D + C}^2$.`\n\n          BC = texNombre(calculANePlusJamaisUtiliser(Math.sqrt(c ** 2 + c ** 2 + c ** 2), 1))\n          reponse = arrondi(Math.sqrt(c ** 2 + c ** 2 + c ** 2), 1)\n          texteCorr += `<br> ${sp(10)}$${A + C}^2=${texNombre(c)}^2+${texNombre(c)}^2$`\n          texteCorr += `<br> ${sp(10)}$${miseEnEvidence(A + C, 'green')}^2=${miseEnEvidence(texNombre(c ** 2 + c ** 2), 'green')}$`\n          texteCorr += `<br> ${sp(10)} No need to find the value of $${A + C}$ because only its square interests us here.`\n          texteCorr += `<br> Let's go back to $${longueurATrouver}^2=${A + B}^2+${A + C}^2$.`\n          texteCorr += `<br> $${longueurATrouver}^2=${texNombre(c)}^2+${miseEnEvidence(texNombre(c ** 2 + c ** 2), 'green')} = ${texNombre(c ** 2 + c ** 2 + c ** 2)}$`\n          texteCorr += `<br> $${longueurATrouver}=\\\\sqrt{${texNombre(c ** 2 + c ** 2 + c ** 2)}}$`\n          texteCorr += `<br> $${longueurATrouver}\\\\approx${miseEnEvidence(BC)}$ ${texteEnCouleurEtGras(listeUnites[j])}`\n          break\n        case 3: // Diagonale de la face d'un pavé droit\n          L = randint(5, 20)\n          h = randint(5, 20, [L])\n          p = randint(5, 20, [L, h])\n          A = point3d(0, 0, 0)\n          B = point3d(L, 0, 0)\n          D = point3d(0, 0, h)\n          choixProfondeur = choice([p, -p])\n          E = point3d(0, choixProfondeur, 0)\n\n          nomSolide = choisitLettresDifferentes(8, 'OQWX').join('')\n          solideDessine = pave3d(A, B, D, E, 'blue', true, nomSolide)\n          choixSegments = []\n          choixSegments.push(['02', '1', L, h], ['13', '2', h, L])\n          if (choixProfondeur > 0) {\n            choixSegments.push(['16', '5', p, h], ['25', '6', p, h]) // Ce sont les diagonales des faces visibles et le sommet qui forme un triangle rectangle\n            if (context.anglePerspective > 0) choixSegments.push(['27', '3', L, p], ['36', '2', L, p])\n            else choixSegments.push(['14', '5', p, L], ['05', '1', L, p])\n          } else {\n            choixSegments.push(['07', '3', h, p], ['34', '0', p, h]) // Ce sont les diagonales des faces visibles et le sommet qui forme un triangle rectangle\n            if (context.anglePerspective < 0) choixSegments.push(['27', '3', L, p], ['36', '2', L, p])\n            else choixSegments.push(['14', '5', p, L], ['05', '1', L, p])\n          }\n\n          segmentChoisi = choice(choixSegments)\n          J = nomSolide[parseInt(segmentChoisi[0][0])]\n          K = nomSolide[parseInt(segmentChoisi[0][1])]\n          I = nomSolide[parseInt(segmentChoisi[1])] // IJK est rectangle en I\n\n          longueurATrouver = J + K\n          texte += `Knowing that in the right box $${nomSolide}$, $${nomSolide[0]}${nomSolide[1]} = ${L}$ ${listeUnites[j]}, $${nomSolide[0]}${nomSolide[3]} = ${h}$ ${listeUnites[j]} and $${nomSolide[0]}${nomSolide[4]} = ${p}$ ${listeUnites[j]}, calculate the length $${longueurATrouver}$, rounded to the tenth of ${listeUnites[j]}.<br>`\n          segmentATrouver = segment(solideDessine.sommets[parseInt(segmentChoisi[0][0])].c2d, solideDessine.sommets[parseInt(segmentChoisi[0][1])].c2d, '#f15929')\n          segmentATrouver.epaisseur = 2\n          objetsEnonce.push(...solideDessine.c2d, segmentATrouver)\n          texte += mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), {\n            scale: context.isHtml ? 0.7 : 0.3,\n            style: 'block'\n          }), objetsEnonce) + '<br>'\n          objetsEnonce.push(new CodageAngleDroit3D(solideDessine.sommets[parseInt(segmentChoisi[0][0])], solideDessine.sommets[parseInt(segmentChoisi[1])], solideDessine.sommets[parseInt(segmentChoisi[0][1])], '#f15929', 2))\n          texteCorr += '<br>' + mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), {\n            scale: context.isHtml ? 0.7 : 0.3,\n            style: 'block'\n          }), objetsEnonce) + '<br>'\n          reponse = arrondi(Math.sqrt(segmentChoisi[2] ** 2 + segmentChoisi[3] ** 2), 1)\n          texteCorr += '<br>' + RedactionPythagore(I, J, K, 1, segmentChoisi[2], segmentChoisi[3], reponse, listeUnites[j])[0]\n\n          break\n        case 4: // Diagonale d'un pavé droit\n          L = randint(5, 20)\n          h = randint(5, 20, [L])\n          p = randint(5, 20, [L, h])\n          A = point3d(0, 0, 0)\n          B = point3d(L, 0, 0)\n          D = point3d(0, 0, h)\n          choixProfondeur = choice([p, -p])\n          E = point3d(0, choixProfondeur, 0)\n\n          nomSolide = choisitLettresDifferentes(8, 'OQWX').join('')\n          solideDessine = pave3d(A, B, D, E, 'blue', true, nomSolide)\n          choixSegments = [['60', '5', '05', '1', p, L, h], ['71', '4', '14', '0', p, L, h],\n            ['24', '1', '41', '0', L, p, h], ['35', '0', '50', '1', L, p, h]] // Ce sont les diagonales du cubes, le sommet qui forme un triangle rectangle, la diagonale d'une face et le sommet qui forme un triangle rectangle avec cette dernière diagonale\n          segmentChoisi = choice(choixSegments)\n          J = nomSolide[parseInt(segmentChoisi[0][0])]\n          K = nomSolide[parseInt(segmentChoisi[0][1])]\n          I = nomSolide[parseInt(segmentChoisi[1])] // IJK est rectangle en I\n          M = nomSolide[parseInt(segmentChoisi[3])] // ACD est rectangle en\n          longueurATrouver = J + K\n          texte += `Knowing that in the right box $${nomSolide}$, $${nomSolide[0]}${nomSolide[1]} = ${L}$ ${listeUnites[j]}, $${nomSolide[0]}${nomSolide[3]} = ${h}$ ${listeUnites[j]} and $${nomSolide[0]}${nomSolide[4]} = ${p}$ ${listeUnites[j]}, calculate the length $${longueurATrouver}$, rounded to the tenth of ${listeUnites[j]}.<br>`\n          segmentATrouver = segment(solideDessine.sommets[parseInt(segmentChoisi[0][0])].c2d, solideDessine.sommets[parseInt(segmentChoisi[0][1])].c2d, '#f15929')\n          segmentATrouver.epaisseur = 2\n          segmentATrouver.pointilles = 2\n          objetsEnonce.push(...solideDessine.c2d, segmentATrouver)\n          texte += mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), {\n            scale: context.isHtml ? 0.7 : 0.3,\n            style: 'block'\n          }), objetsEnonce) + '<br>'\n          segmentAnnexe = segment(solideDessine.sommets[parseInt(segmentChoisi[1])].c2d, solideDessine.sommets[parseInt(segmentChoisi[0][1])].c2d, 'green')\n          segmentAnnexe.epaisseur = 2\n          segmentAnnexe.pointilles = 1\n          objetsEnonce.push(segmentAnnexe)\n          objetsEnonce.push(new CodageAngleDroit3D(solideDessine.sommets[parseInt(segmentChoisi[0][0])], solideDessine.sommets[parseInt(segmentChoisi[1])], solideDessine.sommets[parseInt(segmentChoisi[0][1])], '#f15929', 2))\n          objetsEnonce.push(new CodageAngleDroit3D(solideDessine.sommets[parseInt(segmentChoisi[1])], solideDessine.sommets[parseInt(segmentChoisi[3])], solideDessine.sommets[parseInt(segmentChoisi[0][1])], 'green', 2))\n          texteCorr += '<br>' + mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), {\n            scale: 0.7,\n            style: 'block'\n          }), objetsEnonce) + '<br>'\n          texteCorr += `The triangle $${longueurATrouver + I}$ is right-angled in $${I}$ so according to the Pythagorean theorem, we have:`\n          texteCorr += `$${longueurATrouver}^2=${I + J}^2+${I + K}^2$.`\n          texteCorr += `<br> We cannot continue if we do not know the value of $${I + K}^2$. Let's find it.`\n          texteCorr += `<br> ${sp(10)}The triangle $${K + I + M}$ is right-angled in $${M}$ so according to the Pythagorean theorem, we have:`\n          texteCorr += `$${I + K}^2=${I + M}^2+${M + K}^2$.`\n\n          JK = texNombre(calculANePlusJamaisUtiliser(Math.sqrt(segmentChoisi[4] ** 2 + segmentChoisi[5] ** 2 + segmentChoisi[6] ** 2), 1))\n          reponse = arrondi(Math.sqrt(segmentChoisi[4] ** 2 + segmentChoisi[5] ** 2 + segmentChoisi[6] ** 2), 1)\n          texteCorr += `<br> ${sp(10)}$${I + K}^2=${texNombre(segmentChoisi[4])}^2+${texNombre(segmentChoisi[5])}^2$`\n          texteCorr += `<br> ${sp(10)}$${miseEnEvidence(I + K, 'green')}^2=${miseEnEvidence(texNombre(segmentChoisi[4] ** 2 + segmentChoisi[5] ** 2), 'green')}$`\n          texteCorr += `<br> ${sp(10)} No need to find the value of $${I + K}$ because only its square interests us here.`\n          texteCorr += `<br> Let's go back to $${longueurATrouver}^2=${I + J}^2+${I + K}^2$.`\n          texteCorr += `<br> $${longueurATrouver}^2=${texNombre(segmentChoisi[6])}^2+${miseEnEvidence(texNombre(segmentChoisi[4] ** 2 + segmentChoisi[5] ** 2), 'green')} = ${texNombre(segmentChoisi[6] ** 2 + segmentChoisi[4] ** 2 + segmentChoisi[5] ** 2)}$`\n          texteCorr += `<br> $${longueurATrouver}=\\\\sqrt{${texNombre(segmentChoisi[6] ** 2 + segmentChoisi[4] ** 2 + segmentChoisi[5] ** 2)}}$`\n          texteCorr += `<br> $${longueurATrouver}\\\\approx${miseEnEvidence(JK)}$ ${texteEnCouleurEtGras(listeUnites[j])}`\n          break\n        case 5: // Dans un cylindre\n          r = randint(4, 10)\n          h = randint(5, 15, [r])\n          A = point3d(0, 0, 0, true, choisitLettresDifferentes(1, 'OQWX')[0], 'left')\n          if (choice([0, 1, 2]) === 0) {\n            B = point3d(r, 0, 0)\n            D = point3d(0, 0, h, true, choisitLettresDifferentes(1, 'OQWX' + A.label)[0], 'left')\n          } else if (choice([0, 1]) === 0) {\n            B = point3d(0, r, 0)\n            D = point3d(h, 0, 0, true, choisitLettresDifferentes(1, 'OQWX' + A.label)[0], 'left')\n          } else {\n            B = point3d(0, 0, r)\n            D = point3d(0, h, 0, true, choisitLettresDifferentes(1, 'OQWX' + A.label)[0], 'left')\n          }\n          v = vecteur3d(A, B)\n          solideDessine = cylindre3d(A, D, v, v, 'blue', false, true, true, 'black')\n\n          // To place a point on the visible base but which is not too close to the axis and the two generators.\n          anglesPossibles = shuffle(rangeMinMax(2, solideDessine.pointsBase2.length - 3, [16, 17, 18, 19, 20]))\n          indiceAngleChoisi = 0\n          while (longueur(D.c2d, solideDessine.pointsBase2[anglesPossibles[indiceAngleChoisi]]) < longueur(D.c2d, solideDessine.pointsBase2[0]) / 2) {\n            indiceAngleChoisi++\n          }\n\n          ptBase2 = rotation3d(translation3d(D, v), droite3d(A, vecteur3d(A, D)), solideDessine.angleDepart + 10 * anglesPossibles[indiceAngleChoisi])\n          ptBase2.c2d.nom = choisitLettresDifferentes(1, 'OQWX' + A.label + D.label)[0]\n          longueurATrouver = A.label + ptBase2.c2d.nom\n          segmentATrouver = segment(A.c2d, ptBase2.c2d, '#f15929')\n          segmentATrouver.epaisseur = 2\n          segmentATrouver.pointilles = 2\n          objetsEnonce.push(...solideDessine.c2d, segmentATrouver, tracePoint(ptBase2), labelPoint(A, D, ptBase2.c2d))\n          texte += `In this cylinder of revolution, the radius of its bases (with respective centers $${A.label}$ and $${D.label}$) is $${r}$ ${listeUnites[j]} and its height is $${h}$ ${listeUnites[j]}. Knowing that the point $${ptBase2.c2d.nom}$ is on the base of center $${D.label}$, calculate the length $${longueurATrouver}$, rounded to the tenth of ${listeUnites[j]}.<br>`\n          texte += '<br>' + mathalea2d(Object.assign({}, fixeBordures([...solideDessine.c2d]), {\n            scale: context.isHtml ? 0.7 : 0.3,\n            style: 'block'\n          }), objetsEnonce)\n\n          objetsEnonce.push(new CodageAngleDroit3D(A, D, ptBase2, 'green', 2))\n          segmentAnnexe = segment(D.c2d, ptBase2.c2d, 'green')\n          objetsEnonce.push(segmentAnnexe)\n          segmentAnnexe = segment(D.c2d, A.c2d, 'green')\n          objetsEnonce.push(segmentAnnexe)\n          texteCorr += '<br>' + mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), {\n            scale: context.isHtml ? 0.7 : 0.3,\n            style: 'block'\n          }), objetsEnonce)\n          reponse = arrondi(Math.sqrt(h ** 2 + r ** 2), 1)\n          texteCorr += '<br>' + RedactionPythagore(D.label, A.label, ptBase2.c2d.nom, 1, h, r, reponse, listeUnites[j])[0]\n          break\n        case 6: // Dans une pyramide à base régulière\n          r = randint(4, 10)\n          h = randint(5, 15, [r])\n          A = point3d(0, 0, 0, true, choisitLettresDifferentes(1, 'OQWX')[0], 'left')\n          B = point3d(r, 0, 0)\n          D = point3d(0, 0, h * (1), true, choisitLettresDifferentes(1, 'OQWX' + A.label)[0], 'left')\n          v = vecteur3d(A, B)\n          ptsBase = [B]\n          nbSommets = choice([3, 5, 6, 7])\n          for (let ee = 1; ee < nbSommets; ee++) {\n            // pyramid with non-regular base: ptsBase.push(rotation3d(B, straight3d(A, vector3d(D, A)), ee * 360 / (nbVertices) + choice([-10, 10]) * randint(0, 2)))\n            ptsBase.push(rotation3d(B, droite3d(A, vecteur3d(D, A)), ee * 360 / (nbSommets)))\n          }\n          p = polygone3d(ptsBase, 'blue')\n          solideDessine = pyramide3d(p, D, 'blue', A, true, 'black', true)\n          numeroSommet = randint(0, nbSommets - 1)\n          segmentATrouver = solideDessine.aretesSommet[numeroSommet].c2d\n          segmentATrouver.epaisseur = 2\n          segmentATrouver.color = colorToLatexOrHTML('#f15929')\n          longueurATrouver = D.label + p.listePoints2d[numeroSommet].nom\n          texte += `$${solideDessine.nom}$ is a regular pyramid. The distance between $${A.label}$, the center of the base, and one of the vertices of the base is $${r}$ ${listeUnites[j]} and the height of this pyramid is $${h}$ ${listeUnites[j]}. Calculate the length $${longueurATrouver}$, rounded to the tenth of ${listeUnites[j]}.<br>`\n          texte += mathalea2d(Object.assign({}, fixeBordures([...solideDessine.c2d]), {\n            scale: context.isHtml ? 0.7 : 0.3,\n            style: 'block'\n          }), [...solideDessine.c2d, segmentATrouver])\n\n          objetsEnonce.push(...solideDessine.c2d, segmentATrouver, new CodageAngleDroit3D(D, A, p.listePoints[numeroSommet], 'green', 2))\n          segmentAnnexe = segment(A.c2d, p.listePoints2d[numeroSommet], 'green')\n          objetsEnonce.push(segmentAnnexe)\n          segmentAnnexe = segment(D.c2d, A.c2d, 'green')\n          objetsEnonce.push(segmentAnnexe)\n          texteCorr += '<br>' + mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), {\n            scale: context.isHtml ? 0.7 : 0.3,\n            style: 'block'\n          }), objetsEnonce)\n          reponse = arrondi(Math.sqrt(h ** 2 + r ** 2), 1)\n          texteCorr += '<br>' + RedactionPythagore(A.label, D.label, p.listePoints2d[numeroSommet].nom, 1, h, r, reponse, listeUnites[j])[0]\n          break\n        case 7: // Dans un cône\n          r = randint(4, 10)\n          h = randint(5, 15, [r])\n          A = point3d(0, 0, 0, true, choisitLettresDifferentes(1, 'OQWX')[0], 'left')\n          B = point3d(r, 0, 0)\n          D = point3d(0, 0, h, true, choisitLettresDifferentes(1, 'OQWX' + A.label)[0], 'left')\n          v = vecteur3d(A, B)\n          ptsBase = [B]\n          nbSommets = 36\n          for (let ee = 1; ee < nbSommets; ee++) {\n            ptsBase.push(rotation3d(B, droite3d(A, vecteur3d(D, A)), ee * 360 / (nbSommets)))\n          }\n          p = polygone3d(ptsBase, 'blue')\n          solideDessine = cone3d(A, D, v, 'blue', true, 'black', assombrirOuEclaircir('gray', 100))\n          numeroSommet = randint(1, Math.floor(nbSommets / 2) - 1)\n          if (context.anglePerspective < 0) numeroSommet = (nbSommets - numeroSommet) % nbSommets\n          segmentATrouver = segment(D.c2d, p.listePoints2d[numeroSommet], '#f15929')\n          segmentATrouver.epaisseur = 2\n          texte += `In this cone of revolution, the radius of its base is $${r}$ ${listeUnites[j]} and its height is $${h}$ ${listeUnites[j]}. Calculate the length of a generatrix of this cone, rounded to the tenth of ${listeUnites[j]}.<br>`\n          texte += mathalea2d(Object.assign({}, fixeBordures([...solideDessine.c2d]), {\n            scale: context.isHtml ? 0.7 : 0.3,\n            style: 'block'\n          }), [...solideDessine.c2d, segmentATrouver])\n\n          ptBase = p.listePoints2d[numeroSommet]\n          ptBase.nom = choisitLettresDifferentes(1, 'OQWX' + A.label + D.label)[0]\n          ptBase.positionLabel = 'below'\n          longueurATrouver = D.label + ptBase.nom\n          objetsEnonce.push(...solideDessine.c2d, segmentATrouver, new CodageAngleDroit3D(D, A, p.listePoints[numeroSommet], 'green', 2))\n          segmentAnnexe = segment(A.c2d, p.listePoints2d[numeroSommet], 'green')\n          objetsEnonce.push(segmentAnnexe)\n          segmentAnnexe = segment(D.c2d, A.c2d, 'green')\n          objetsEnonce.push(segmentAnnexe)\n          objetsEnonce.push(labelPoint(ptBase, D.c2d))\n          texteCorr += '<br>' + mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), {\n            scale: context.isHtml ? 0.7 : 0.3,\n            style: 'block'\n          }), objetsEnonce)\n          reponse = arrondi(Math.sqrt(h ** 2 + r ** 2), 1)\n          texteCorr += '<br>' + RedactionPythagore(A.label, D.label, ptBase.nom, 1, h, r, reponse, listeUnites[j])[0]\n          break\n        case 8: // Rayon dans une sphère\n          context.anglePerspective = randint(2, 6) * choice([10, -10])\n          r = randint(4, 10)\n          choixProfondeur = choice([1, 2, 4])\n          r2 = r * Math.cos(choixProfondeur / 6 * Math.PI / 2)\n          A = point3d(0, 0, 0, true, choisitLettresDifferentes(1, 'OQWX')[0], 'left')\n          h = A.z + r * Math.sin(choixProfondeur / 6 * Math.PI / 2)\n          B = point3d(r2, A.y, h, true)\n          B = rotation3d(B, droite3d(A, vecteur3d(0, 0, 1)), context.anglePerspective < 0 ? 30 : -30)\n          B.label = choisitLettresDifferentes(1, 'OQWX' + A.label)[0]\n          B.c2d.nom = B.label\n          B.c2d.positionLabel = 'below'\n          D = point3d(0, A.y, h, true, choisitLettresDifferentes(1, 'OQWX' + A.label + B.label)[0])\n          longueurATrouver = B.label + A.label\n          segmentATrouver = segment(A.c2d, B.c2d, '#f15929')\n          segmentATrouver.epaisseur = 2\n          segmentATrouver.pointilles = 2\n          segmentAnnexe = segment(D.c2d, B.c2d, 'black')\n          segmentAnnexe.pointilles = 2\n          h = arrondi(h, 1)\n          r2 = arrondi(r2, 1)\n          sph = sphere3d(A, r, 'green', 'blue', 12, 'lightgray', 0, 'black', true)\n          objetsEnonce = sph.c2d\n          objetsEnonce.push(segmentATrouver, segmentAnnexe, tracePoint(B, D, A), labelPoint(A, D, B), new CodageAngleDroit3D(A, D, B, 'black', 1))\n          texte += `$${B.label}$ belongs to this sphere with center $${A.label}$. $${D.label}$ is a point inside the sphere, $${texNombre(h)}$ ${listeUnites[j]} from $${A.label}$ and the distance between $${B.label}$ and $${D.label}$ is $${texNombre(r2)}$ ${listeUnites[j]}. Calculate the radius of the sphere, rounded to the tenth of ${listeUnites[j]}.<br>`\n          texte += mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), {\n            scale: context.isHtml ? 0.7 : 0.3,\n            style: 'block'\n          }), objetsEnonce)\n          objetsEnonce = sph.c2d\n          segmentAnnexe.epaisseur = 2\n          segmentAnnexe.color = colorToLatexOrHTML('green')\n          objetsEnonce.push(segmentATrouver, segmentAnnexe, tracePoint(B, D, A), labelPoint(A, D, B), new CodageAngleDroit3D(A, D, B, 'green', 1))\n          segmentAnnexe = segment(D.c2d, A.c2d, 'green')\n          segmentAnnexe.epaisseur = 2\n          segmentAnnexe.pointilles = 2\n          objetsEnonce.push(segmentAnnexe)\n          texteCorr += '<br>' + mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), {\n            scale: context.isHtml ? 0.7 : 0.3,\n            style: 'block'\n          }), objetsEnonce)\n          reponse = arrondi(Math.sqrt(h ** 2 + r2 ** 2), 1)\n          texteCorr += '<br>' + RedactionPythagore(D.label, A.label, B.label, 1, h, r2, reponse, listeUnites[j])[0]\n          break\n        case 9: // Hauteur dans une sphère\n          context.anglePerspective = randint(2, 6) * choice([10, -10])\n          r = randint(4, 10)\n          choixProfondeur = choice([1, 2, 4])\n          r2 = r * Math.cos(choixProfondeur / 6 * Math.PI / 2)\n          A = point3d(0, 0, 0, true, choisitLettresDifferentes(1, 'OQWX')[0], 'left')\n          h = A.z + r * Math.sin(choixProfondeur / 6 * Math.PI / 2)\n          B = point3d(r2, A.y, h, true)\n          B = rotation3d(B, droite3d(A, vecteur3d(0, 0, 1)), context.anglePerspective < 0 ? 30 : -30)\n          B.label = choisitLettresDifferentes(1, 'OQWX' + A.label)[0]\n          B.c2d.nom = B.label\n          B.c2d.positionLabel = 'below'\n          D = point3d(0, A.y, h, true, choisitLettresDifferentes(1, 'OQWX' + A.label + B.label)[0])\n          longueurATrouver = B.label + D.label\n          segmentATrouver = segment(D.c2d, B.c2d, '#f15929')\n          segmentATrouver.epaisseur = 2\n          segmentATrouver.pointilles = 2\n          h = arrondi(h, 1)\n          sph = sphere3d(A, r, 'green', 'blue', 12, 'lightgray', 0, 'black', true)\n          objetsEnonce = sph.c2d\n          objetsEnonce.push(segmentATrouver, tracePoint(B, D, A), labelPoint(A, D, B), new CodageAngleDroit3D(A, D, B, 'black', 1))\n          texte += `$${B.label}$ belongs to this sphere with center $${A.label}$ and radius $${texNombre(r)}$ ${listeUnites[j]}. $${D.label}$ is a point inside the sphere, at $${texNombre(h)}$ ${listeUnites[j]} of $${A.label}$. Calculate the distance between $${B.label}$ and $${D.label}$, rounded to the tenth of ${listeUnites[j]}.<br>`\n          texte += mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), {\n            scale: context.isHtml ? 0.7 : 0.3,\n            style: 'block'\n          }), objetsEnonce)\n\n          objetsEnonce = sph.c2d\n          segmentAnnexe = segment(D.c2d, A.c2d, 'green')\n          segmentAnnexe.epaisseur = 2\n          segmentAnnexe.pointilles = 2\n          objetsEnonce.push(segmentATrouver, segmentAnnexe, tracePoint(B, D, A), labelPoint(A, D, B), new CodageAngleDroit3D(A, D, B, 'green', 1))\n          segmentAnnexe = segment(B.c2d, A.c2d, 'green')\n          segmentAnnexe.epaisseur = 2\n          segmentAnnexe.pointilles = 2\n          objetsEnonce.push(segmentAnnexe)\n          texteCorr += '<br>' + mathalea2d(Object.assign({}, fixeBordures(objetsEnonce), {\n            scale: context.isHtml ? 0.7 : 0.3,\n            style: 'block'\n          }), objetsEnonce)\n          reponse = arrondi(Math.sqrt(r ** 2 - h ** 2), 1)\n          texteCorr += '<br>' + RedactionPythagore(D.label, B.label, A.label, 2, reponse, h, r, listeUnites[j])[0]\n          break\n      }\n      setReponse(this, i, new Grandeur(reponse, listeUnites[j]), { formatInteractif: 'units' })\n      if (this.interactif && context.isHtml) texte += `<br>$${longueurATrouver}\\\\approx$` + ajouteChampTexteMathLive(this, i, 'width25 inline units[lengths]')\n\n      if (context.isAmc) {\n        this.autoCorrection[i] = {\n          enonce: texte,\n          enonceAvant: this.sup2 === 2,\n          options: {\n            ordered: false\n          }\n        }\n        this.autoCorrection[i].propositions = []\n        if (this.sup2 === 1) {\n          this.autoCorrection[i].propositions.push(\n            {\n              type: 'AMCNum',\n              propositions: [\n                {\n                  reponse: { // utilisé si type = 'AMCNum'\n                    texte,\n                    valeur: [reponse], // obligatoire (la réponse numérique à comparer à celle de l'élève). EE : Si une fraction est la réponse, mettre un tableau sous la forme [num,den]\n                    alignement: 'center', // EE : ce champ est facultatif et n'is functional only for the hybrid. It allows you to choose where the boxes are arranged on the sheet. By default, it is like the text before it. To put left, center or right, choose from ('flushleft', 'center', 'flushright').\n                    param: {\n                      digits: nombreDeChiffresDe(reponse), // obligatoire pour AMC (le nombre de chiffres dans le nombre, si digits est mis à 0, alors il sera déterminé pour coller au nombre décimal demandé)\n                      decimals: 1, // obligatoire pour AMC (le nombre de chiffres dans la partie décimale du nombre, si decimals est mis à 0, alors il sera déterminé pour coller au nombre décimal demandé)\n                      signe: false // obligatoire pour AMC (présence d'une case + ou -)\n                    }\n                  }\n                }\n              ]\n            }\n          )\n        } else {\n          this.autoCorrection[i].propositions.push(\n            {\n              type: 'AMCOpen',\n              propositions: [\n                {\n                  texte: texteCorr,\n                  statut: 4, // OBLIGATOIRE (ici c'is the number of lines of the frame for the answer of the'élève sur AMC)\n                  enonce: texte,\n                  sanscadre: false, // EE : ce champ est facultatif et permet (si true) de cacher le cadre et les lignes acceptant la réponse de l'élève\n                  pointilles: false // EE : ce champ est facultatif et permet (si false) d'enlever les pointillés sur chaque ligne.\n                }\n              ]\n            }\n          )\n        }\n      }\n\n      if (this.questionJamaisPosee(i, nomSolide, r, h)) {\n        // If the question has never been asked, we create another one\n        this.listeQuestions.push(texte)\n        this.listeCorrections.push(texteCorr)\n        i++\n      }\n      cpt++\n    }\n    listeQuestionsToContenu(this)\n  }\n  if (context.isAmc) this.besoinFormulaire2Numerique = ['AMC exercise', 2, '1: Open question\\n2: Numerical response']\n  this.besoinFormulaireTexte = ['Type of length to find', 'Numbers separated by hyphens\\n1: Diagonal of a face of a cube\\n2: Diagonal of a cube\\n3: Diagonal of a face of a straight block\\n4: Diagonal of\\n a straight block\\n5: In a cylinder\\n6: In a pyramid\\n7: In a cone\\n8: Radius of a sphere\\n9: Radius of a section of a sphere\\n10: 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