{"version":3,"file":"6M21-uFDNdCJW.js","sources":["../../src/exercices/6e/6M21.js"],"sourcesContent":["import { arc } from '../../lib/2d/cercle.js'\nimport { codageSegment } from '../../lib/2d/codages.js'\nimport { droite, droiteParPointEtPente } from '../../lib/2d/droites.js'\nimport { milieu, point, pointIntersectionDD, pointSurSegment } from '../../lib/2d/points.js'\nimport { polygone } from '../../lib/2d/polygones.js'\nimport { longueur, segment, vecteur } from '../../lib/2d/segmentsVecteurs.js'\nimport { homothetie, projectionOrtho, rotation, translation } from '../../lib/2d/transformations.js'\nimport { choice, combinaisonListes } from '../../lib/outils/arrayOutils'\nimport { arrondi } from '../../lib/outils/nombres'\nimport { numAlpha } from '../../lib/outils/outilString.js'\nimport Exercice from '../deprecatedExercice.js'\nimport { mathalea2d, colorToLatexOrHTML, ObjetMathalea2D } from '../../modules/2dGeneralites.js'\nimport { listeQuestionsToContenu, randint, entreDeux, gestionnaireFormulaireTexte } from '../../modules/outils.js'\nimport { min, max } from 'mathjs'\nimport { propositionsQcm } from '../../lib/interactif/qcm.js'\nimport { context } from '../../modules/context.js'\nimport { afficherTempo, cacherTempo } from '../../modules/2dAnimation.js'\nexport const dateDePublication = '08/06/2022'\nexport const titre = 'Compare perimeters and/or areas of figures'\nexport const interactifReady = true\nexport const interactifType = 'qcm'\n\n/**\n * Comparer aires et/ou périmètres de figures avec ceux d'un rectangle référence\n * Ref 6M21\n * @author Eric Elter\n * Publié le 08/06/2022\n */\nfunction TranslationPuisRotationAnimee (numId, figure1, v, figure2, O, angle, t1 = 5, t2 = 2) {\n  ObjetMathalea2D.call(this, { })\n  this.svg = function (coeff) {\n    afficherTempo(figure2, t1, t1 + t2, 1)\n    let code = '<g> '\n    // Translation de figure1 de vecteur v\n    if (Array.isArray(figure1)) { // Si la figure1 est constituée d'une liste d'éléments\n      for (const objet of figure1) {\n        code += '\\n' + objet.svg(coeff)\n      }\n    } else { // Si la figure1 n'est constituée que d'un élément\n      code += '\\n' + figure1.svg(coeff)\n    }\n    code += `<animateTransform\n    attributeName=\"transform\"\n    attributeType=\"XML\"\n    type=\"translate\"\n    from=\"0 0\"\n    to=\"${arrondi(v.xSVG(coeff), 0)} ${arrondi(v.ySVG(coeff), 0)}\"\n    begin=\"0s\" dur=\"${t1}s\" fill=\"freeze\"  repeatCount=\"1\" id=\"translat${numId}\"\n    /></path></g>`\n\n    cacherTempo(figure1, t1, 0, 1)\n\n    // Rotation de figure2 de centre O et de angle angle\n    code += '<g>'\n    if (Array.isArray(figure2)) { // Si la figure2 est constituée d'une liste d'éléments\n      for (const objet of figure2) {\n        code += '\\n' + objet.svg(coeff)\n      }\n    } else { // Si la figure2 n'est constituée que d'un élément\n      code += '\\n' + figure2.svg(coeff)\n    }\n    code += `<animateTransform\n  attributeName=\"transform\"\n  type=\"rotate\"\n  from=\"0 ${O.xSVG(coeff)} ${O.ySVG(coeff)}\"\n  to=\"${-angle} ${O.xSVG(coeff)} ${O.ySVG(coeff)}\"\n  begin=\"translat${numId}.end\" dur=\"${t2}s\" fill=\"freeze\" repeatCount=\"1\" id=\"rotat-${numId}\"\n  /></path>`\n\n    code += '</g>'\n    return code\n  }\n}\nfunction translationPuisRotationAnimees (...args) {\n  return new TranslationPuisRotationAnimee(...args)\n}\n\nexport const uuid = '95313'\nexport const ref = '6M21'\nexport default function CompareAireEtPerimetreAvecRectangle () {\n  Exercice.call(this)\n  this.titre = titre\n  this.consigne = ''\n  this.nbQuestions = 3\n  this.nbCols = 1\n  this.nbColsCorr = 1\n  this.spacingCorr = 1\n  this.sup = 13\n  this.sup2 = 3\n\n  this.nouvelleVersion = function () {\n    this.listeQuestions = [] // tableau contenant la liste des questions\n    this.listeCorrections = []\n    this.autoCorrection = []\n    /*\n    let typesDeProblemes = []\n    const nbQuestionsDifferentes = 13\n    if (typeof this.sup === 'number') {\n      // If it is a number then there is only one choice for the number of steps\n      typesDeProblemes[0] = contraindreValeur(1, nbQuestionsDifferentes, this.sup, nbQuestionsDifferentes)\n    } else {\n      typesDeProblemes = this.sup.split('-') // Sinon on crée un tableau à partir des valeurs séparées par des -\n      for (let i = 0; i < typesDeProblemes.length; i++) {\n        typesDeProblemes[i] = contraindreValeur(1, nbQuestionsDifferentes, parseInt(typesDeProblemes[i]), nbQuestionsDifferentes)\n      }\n    }\n    if (compteOccurences(typesDeProblemes, 13) > 0) typesDeProblemes = rangeMinMax(1, 12) // Teste si l'utilisateur a choisi tout\n\n    typesDeProblemes = combinaisonListes(typesDeProblemes, this.nbQuestions)\n    */\n    const typesDeProblemes = gestionnaireFormulaireTexte({\n      max: 12,\n      defaut: 13,\n      melange: 13,\n      nbQuestions: this.nbQuestions,\n      saisie: this.sup\n    })\n\n    const color = combinaisonListes(['red', 'blue', 'green', 'gray', 'pink', '#f15929'], this.nbQuestions)\n\n    let aireOuPerimetre = 'Both'\n    if (this.sup2 === 1) aireOuPerimetre = 'Perimeter'\n    else if (this.sup2 === 2) aireOuPerimetre = 'Area'\n\n    let compteurInteractif = 0\n    for (let q = 0, cpt = 0, A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T,\n      rayonOuCote, pt1, pt2, figAire1, figAire2, figAireCorr, figAireCorr2, figAire2Corr, choixFig, choixFig2, choixFigAire2, angleCorr,\n      aleaAngle, aleaLongueur, aleaRayon, aleaDemiDisque, aleaPente, aleaRapportHomothetie, d1, d2, d3, d4, poly, rect,\n      objets, texte, texteCorr, paramsEnonce, monQcmPerimetre, monQcmAire, hauteur,\n      reponsePerimetre1, reponsePerimetre2, reponsePerimetre3, reponseAire1, reponseAire2, reponseAire3;\n      q < this.nbQuestions && cpt < 50;) {\n      objets = []\n      A = point(0, 0)\n      B = point(randint(5, 10), 0)\n      C = point(B.x, randint(5, 10, B.x))\n      D = point(0, C.y)\n      rect = polygone([A, B, C, D])\n      rect.hachures = true\n      rect.pointilles = 2\n      reponsePerimetre1 = false\n      reponsePerimetre2 = false\n      reponsePerimetre3 = false\n      reponseAire1 = false\n      reponseAire2 = false\n      reponseAire3 = false\n\n      if (this.sup2 === 4) aireOuPerimetre = choice(['Area', 'Perimeter'])\n\n      switch (typesDeProblemes[q]) {\n        case 1 : // Polygone inscrit dans rectangle\n          E = A\n          G = point(entreDeux((A.x + B.x) / 2, B.x), A.y)\n          F = point(entreDeux(E.x, G.x), entreDeux(A.y, A.y + (D.y + A.y) / 2))\n          H = point(entreDeux(G.x, B.x), entreDeux(A.y, A.y + (D.y + A.y) / 2))\n          I = B\n          J = point(entreDeux(H.x, B.x), entreDeux(H.y, C.y))\n          K = point(B.x, entreDeux(J.y, C.y))\n          L = point(entreDeux(A.x + (A.x + B.x) / 2, B.x), entreDeux(K.y, C.y))\n          M = C\n          N = point(entreDeux(A.x + (A.x + B.x) / 2, L.x), entreDeux(L.y, D.y))\n          O = point(entreDeux(D.x, N.x), D.y)\n          P = point(entreDeux(D.x, O.x), entreDeux(D.y, A.y + (D.y + A.y) / 2))\n          Q = D\n          R = point(entreDeux(A.x, P.x), entreDeux(P.y, A.y + (D.y + A.y) / 2))\n          T = point(entreDeux(A.x, F.x), entreDeux(F.y, A.y + (D.y + A.y) / 2))\n          S = point(A.x, entreDeux(R.y, T.y))\n\n          poly = polygone(E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T)\n          poly.couleurDeRemplissage = colorToLatexOrHTML(color[q])\n          poly.opaciteDeRemplissage = 0.5\n          objets.push(poly, rect)\n          // objects.push(rect)\n          paramsEnonce = { xmin: -0.5, ymin: -0.5, xmax: B.x + 0.5, ymax: C.y + 0.5, pixelsParCm: 30, scale: 0.7, mainlevee: false }\n          texte = mathalea2d(paramsEnonce, objets)\n          // Correction\n          texteCorr = (this.sup2 === 3) ? numAlpha(0) : ''\n          texteCorr += (this.sup2 === 1 || this.sup2 === 3 || aireOuPerimetre !== 'Area') ? 'You have to cover more ground to go around the colored figure than around the hatched rectangle. Therefore, the colored figure has a larger perimeter than that of the hatched rectangle.' : ''\n          texteCorr += (this.sup2 === 3) ? '<br>' + numAlpha(1) : ''\n          texteCorr += (this.sup2 === 2 || this.sup2 === 3 || aireOuPerimetre !== 'Perimeter') ? 'The hatched rectangle covers more area than the colored figure. Therefore, the hatched rectangle has an area greater than that of the colored figure.' : ''\n          // Interactive MCQ\n          if (this.interactif) {\n            reponsePerimetre2 = true\n            reponseAire1 = true\n          }\n          break\n        case 2: // Rectangle inscrit dans polygone\n          E = A\n          G = point(entreDeux((A.x + B.x) / 2, B.x), A.y)\n          F = point(entreDeux(E.x, G.x), entreDeux(A.y, A.y - (D.y + A.y) / 2))\n          H = point(entreDeux(G.x, B.x), entreDeux(A.y, A.y - (D.y + A.y) / 2))\n          I = B\n          J = point(entreDeux(B.x, B.x + (A.x + B.x) / 2), entreDeux(I.y, (I.y + C.y) / 2))\n          K = point(B.x, entreDeux(B.y, C.y))\n          L = point(entreDeux(B.x, J.x), C.y)\n          N = point(entreDeux(D.x, (C.x + D.x) / 2), C.y)\n          M = point(entreDeux(N.x, L.x), entreDeux(D.y, D.y + (D.y + A.y) / 2))\n          O = point(entreDeux(D.x, N.x), entreDeux(D.y, D.y + (D.y + A.y) / 2))\n          P = point(entreDeux(A.x - (A.x + B.x) / 2, A.x), D.y)\n          Q = point(A.x, entreDeux(A.y, D.y))\n          R = point(entreDeux(A.x - (A.x + B.x) / 2, A.x), entreDeux(Q.y, A.y))\n          poly = polygone(E, F, G, H, I, J, K, L, M, N, O, P, Q, R)\n          poly.couleurDeRemplissage = colorToLatexOrHTML(color[q])\n          poly.opaciteDeRemplissage = 0.5\n          objets.push(poly, rect)\n          paramsEnonce = { xmin: min(P.x, R.x) - 0.5, ymin: min(F.y, H.y) - 0.5, xmax: max(J.x, L.x) + 0.5, ymax: max(M.y, O.y) + 0.5, pixelsParCm: 30, scale: 0.7, mainlevee: false }\n          texte = mathalea2d(paramsEnonce, objets)\n          // Correction\n          texteCorr = (this.sup2 === 3) ? numAlpha(0) : ''\n          texteCorr += (this.sup2 === 1 || this.sup2 === 3 || aireOuPerimetre !== 'Area') ? 'You have to cover more ground to go around the colored figure than around the hatched rectangle. Therefore, the colored figure has a larger perimeter than that of the hatched rectangle.' : ''\n          texteCorr += (this.sup2 === 3) ? '<br>' + numAlpha(1) : ''\n          texteCorr += (this.sup2 === 2 || this.sup2 === 3 || aireOuPerimetre !== 'Perimeter') ? 'The hatched rectangle covers less area than the colored figure. Therefore, the colored figure has an area greater than that of the hatched rectangle.' : ''\n          // Interactive MCQ\n          if (this.interactif) {\n            reponsePerimetre2 = true\n            reponseAire2 = true\n          }\n          break\n        case 3: // Deux demi-disques alternés qui s'emboîtent\n          E = point(entreDeux(A.x, A.x + (B.x - A.x) / 3), A.y)\n          F = point(entreDeux(B.x, A.x + 2 * (B.x - A.x) / 3), A.y)\n          G = point(B.x, entreDeux(B.y, B.y + (C.y - B.y) / 3))\n          H = point(B.x, entreDeux(C.y, B.y + 2 * (C.y - B.y) / 3))\n          I = point(entreDeux(B.x, A.x + 2 * (B.x - A.x) / 3), D.y)\n          J = point(entreDeux(A.x, A.x + (B.x - A.x) / 3), D.y)\n          K = point(A.x, entreDeux(C.y, B.y + 2 * (C.y - B.y) / 3))\n          L = point(A.x, entreDeux(B.y, B.y + (C.y - B.y) / 3))\n          poly = polygone(A, B, C, D)\n          poly.couleurDeRemplissage = colorToLatexOrHTML(color[q])\n          poly.opaciteDeRemplissage = 0.5\n          poly.color = 'none'\n          objets.push(poly)\n          rayonOuCote = arrondi((min(longueur(E, F), longueur(G, H), longueur(I, J), longueur(K, L))) / 2)\n          M = translation(E, vecteur(rayonOuCote, 0))\n          N = translation(G, vecteur(0, rayonOuCote))\n          O = translation(I, vecteur(-rayonOuCote, 0))\n          P = translation(K, vecteur(0, -rayonOuCote))\n          paramsEnonce = { xmin: -0.5, ymin: -0.5, xmax: B.x + 0.5, ymax: C.y + 0.5, pixelsParCm: 30, scale: 0.7, mainlevee: false }\n          choixFig = randint(0, 3)\n          switch (choixFig) {\n            case 0:\n              pt1 = M\n              pt2 = E\n              paramsEnonce.ymin = -0.5 - rayonOuCote\n              break\n            case 1:\n              pt1 = N\n              pt2 = G\n              paramsEnonce.xmax = rayonOuCote + B.x + 0.5\n              break\n            case 2:\n              pt1 = O\n              pt2 = I\n              paramsEnonce.ymax = rayonOuCote + C.y + 0.5\n              break\n            case 3:\n              pt1 = P\n              pt2 = K\n              paramsEnonce.xmin = -0.5 - rayonOuCote\n              break\n          }\n\n          figAire1 = arc(pt2, pt1, 180, false, color[q], 'black', 0.5)\n          choixFig2 = randint(0, 3, [choixFig])\n          choixFigAire2 = [\n            [E, M],\n            [G, N],\n            [I, O],\n            [K, P]\n          ]\n          if (choixFig2 === 1) paramsEnonce.xmax = rayonOuCote + B.x + 0.5\n          if (choixFig2 === 3) paramsEnonce.xmin = -0.5 - rayonOuCote\n\n          figAire2 = arc(choixFigAire2[choixFig2][0], choixFigAire2[choixFig2][1], -180, false, 'white', 'black', 1.1)\n          M = rotation(pt2, pt1, 60)\n          N = segment(M, pt1, 'black')\n          N.epaisseur = 2\n          O = rotation(choixFigAire2[choixFig2][0], choixFigAire2[choixFig2][1], -60)\n          P = segment(O, choixFigAire2[choixFig2][1], 'black')\n          P.epaisseur = 2\n          objets.push(figAire1, figAire2, N, codageSegment(M, pt1, '|||'), P, codageSegment(O, choixFigAire2[choixFig2][1], '|||'), rect)\n          texte = mathalea2d(paramsEnonce, objets)\n          // Correction\n          texteCorr = (this.sup2 === 3) ? numAlpha(0) : ''\n          texteCorr += (this.sup2 === 1 || this.sup2 === 3 || aireOuPerimetre !== 'Area') ? 'You have to cover more ground to go around the colored figure than around the hatched rectangle. Therefore, the colored figure has a larger perimeter than that of the hatched rectangle.' : ''\n          texteCorr += (this.sup2 === 3) ? '<br>' + numAlpha(1) : ''\n          texteCorr += (this.sup2 === 2 || this.sup2 === 3 || aireOuPerimetre !== 'Perimeter') ? 'The hatched rectangle covers as much surface as the colored figure. Therefore, the colored figure has an area equal to that of the hatched rectangle.' : ''\n          if ((this.sup2 === 2 || this.sup2 === 3 || aireOuPerimetre !== 'Perimeter')) {\n            objets = []\n            figAire1 = arc(pt2, pt1, 180, false, 'white', 'black', 1.1)\n            figAireCorr = arc(pt2, pt1, 180, false, color[q], 'black', 0.5)\n            angleCorr = choixFig2 - choixFig < 0 ? choixFig2 - choixFig + 4 : choixFig2 - choixFig\n            angleCorr = angleCorr === 1 ? 90 : angleCorr === 2 ? 0 : -90\n            figAireCorr2 = arc(rotation(choixFigAire2[choixFig2][0], choixFigAire2[choixFig2][1], angleCorr), choixFigAire2[choixFig2][1], -180, false, color[q], 'black', 0.5)\n            objets.push(poly, figAire1, figAire2, N, codageSegment(M, pt1, '|||'), P, codageSegment(O, choixFigAire2[choixFig2][1], '|||'), rect)\n            objets.push(translationPuisRotationAnimees(q, figAireCorr, vecteur(pt1, choixFigAire2[choixFig2][1]), figAireCorr2, choixFigAire2[choixFig2][1], -angleCorr))\n            paramsEnonce.ymin = choixFig2 === 0 ? -0.5 - rayonOuCote : paramsEnonce.ymin\n            paramsEnonce.ymax = choixFig2 === 2 ? rayonOuCote + C.y + 0.5 : paramsEnonce.ymax\n            texteCorr += '<br>' + mathalea2d(paramsEnonce, objets)\n            if (context.isHtml) {\n              texteCorr += `<br><button class='btn ui labeled icon button'  style='margin:10px' onclick=\"document.getElementById('${figAireCorr.id}').style.visibility = 'visible',document.getElementById('${figAireCorr2.id}').style.visibility = 'hidden',\n              setTimeout(function() {document.getElementById('${figAireCorr.id}').style.visibility = 'hidden'}, 5000),\n              setTimeout(function() {document.getElementById('${figAireCorr2.id}').style.visibility = \"visible'}, 5000),document.getElementById('translat${q}\").beginElement()\"><i class=\"redo circle icon\"></i>Restart area comparison animation </button>`\n            }\n          }\n          // Interactive MCQ\n          if (this.interactif) {\n            reponsePerimetre2 = true\n            reponseAire3 = true\n          }\n          break\n        case 4: // Deux demi-disques alternés qui ne s'emboîtent pas\n          E = point(entreDeux(A.x, A.x + (B.x - A.x) / 3), A.y)\n          F = point(entreDeux(B.x, A.x + 2 * (B.x - A.x) / 3), A.y)\n          G = point(B.x, entreDeux(B.y, B.y + (C.y - B.y) / 3))\n          H = point(B.x, entreDeux(C.y, B.y + 2 * (C.y - B.y) / 3))\n          I = point(entreDeux(B.x, A.x + 2 * (B.x - A.x) / 3), D.y)\n          J = point(entreDeux(A.x, A.x + (B.x - A.x) / 3), D.y)\n          K = point(A.x, entreDeux(C.y, B.y + 2 * (C.y - B.y) / 3))\n          L = point(A.x, entreDeux(B.y, B.y + (C.y - B.y) / 3))\n          poly = polygone(A, B, C, D)\n          poly.couleurDeRemplissage = colorToLatexOrHTML(color[q])\n          poly.opaciteDeRemplissage = 0.5\n          poly.color = 'none'\n          objets.push(poly)\n          aleaDemiDisque = choice([true, false])\n          aleaRayon = randint(2, 3)\n          rayonOuCote = arrondi((min(longueur(E, F), longueur(G, H), longueur(I, J), longueur(K, L))) / 2)\n          rayonOuCote = aleaDemiDisque ? rayonOuCote : rayonOuCote / aleaRayon\n          M = translation(E, vecteur(rayonOuCote, 0))\n          N = translation(G, vecteur(0, rayonOuCote))\n          O = translation(I, vecteur(-rayonOuCote, 0))\n          P = translation(K, vecteur(0, -rayonOuCote))\n          paramsEnonce = { xmin: -0.5, ymin: -0.5, xmax: B.x + 0.5, ymax: C.y + 0.5, pixelsParCm: 30, scale: 0.7, mainlevee: false }\n          choixFig = randint(0, 3)\n          switch (choixFig) {\n            case 0:\n              pt1 = M\n              pt2 = E\n              paramsEnonce.ymin = -0.5 - rayonOuCote\n              break\n            case 1:\n              pt1 = N\n              pt2 = G\n              paramsEnonce.xmax = rayonOuCote + B.x + 0.5\n              break\n            case 2:\n              pt1 = O\n              pt2 = I\n              paramsEnonce.ymax = rayonOuCote + C.y + 0.5\n              break\n            case 3:\n              pt1 = P\n              pt2 = K\n              paramsEnonce.xmin = -0.5 - rayonOuCote\n              break\n          }\n          figAire1 = arc(pt2, pt1, 180, false, color[q], 'black', 0.5)\n          choixFig2 = randint(0, 3, [choixFig])\n          choixFigAire2 = [\n            [E, M],\n            [G, N],\n            [I, O],\n            [K, P]\n          ]\n          paramsEnonce.xmax = choixFig2 === 1 ? rayonOuCote + B.x + 0.5 : paramsEnonce.xmax\n          paramsEnonce.xmin = choixFig2 === 3 ? -0.5 - rayonOuCote : paramsEnonce.xmin\n          figAire2 = arc(aleaDemiDisque ? homothetie(choixFigAire2[choixFig2][1], choixFigAire2[choixFig2][0], 1 / aleaRayon) : choixFigAire2[choixFig2][0], aleaDemiDisque ? choixFigAire2[choixFig2][1] : homothetie(choixFigAire2[choixFig2][1], choixFigAire2[choixFig2][0], aleaRayon), -180, false, 'white', 'black', 1.1)\n          objets.push(figAire1, figAire2, rect)\n          texte = mathalea2d(paramsEnonce, objets)\n          // Correction\n          texteCorr = (this.sup2 === 3) ? numAlpha(0) : ''\n          texteCorr += (this.sup2 === 1 || this.sup2 === 3 || aireOuPerimetre !== 'Area') ? 'You have to cover more ground to go around the colored figure than around the hatched rectangle. Therefore, the colored figure has a larger perimeter than that of the hatched rectangle.' : ''\n          texteCorr += (this.sup2 === 3) ? '<br>' + numAlpha(1) : ''\n          texteCorr += aleaDemiDisque\n            ? ((this.sup2 === 2 || this.sup2 === 3 || aireOuPerimetre !== 'Perimeter') ? 'The hatched rectangle covers less area than the colored figure. Therefore, the colored figure has an area greater than that of the hatched rectangle.' : '')\n            : ((this.sup2 === 2 || this.sup2 === 3 || aireOuPerimetre !== 'Perimeter') ? 'The hatched rectangle covers more area than the colored figure. Therefore, the hatched rectangle has an area greater than that of the colored figure.' : '')\n          if ((this.sup2 === 2 || this.sup2 === 3 || aireOuPerimetre !== 'Perimeter')) {\n            objets = []\n            figAire1 = arc(pt2, pt1, 180, false, 'white', 'black', 1.1)\n            figAireCorr = arc(pt2, pt1, 180, false, color[q], 'black', 0.5)\n            angleCorr = choixFig2 - choixFig < 0 ? choixFig2 - choixFig + 4 : choixFig2 - choixFig\n            angleCorr = angleCorr === 1 ? 90 : angleCorr === 2 ? 0 : -90\n            figAireCorr2 = arc(rotation(choixFigAire2[choixFig2][0], choixFigAire2[choixFig2][1], angleCorr), choixFigAire2[choixFig2][1], -180, false, color[q], 'black', 0.5)\n            objets.push(poly, figAire1, figAire2, rect)\n            objets.push(translationPuisRotationAnimees(q, figAireCorr, vecteur(pt1, choixFigAire2[choixFig2][1]), figAireCorr2, choixFigAire2[choixFig2][1], -angleCorr))\n            paramsEnonce.ymin = choixFig2 === 0 ? -0.5 - rayonOuCote : paramsEnonce.ymin\n            paramsEnonce.ymax = choixFig2 === 2 ? rayonOuCote + C.y + 0.5 : paramsEnonce.ymax\n            texteCorr += '<br>' + mathalea2d(paramsEnonce, objets)\n            if (context.isHtml) {\n              texteCorr += `<br><button class='btn ui labeled icon button'  style='margin:10px' onclick=\"document.getElementById('${figAireCorr.id}').style.visibility = 'visible',document.getElementById('${figAireCorr2.id}').style.visibility = 'hidden',\n              setTimeout(function() {document.getElementById('${figAireCorr.id}').style.visibility = 'hidden'}, 5000),\n              setTimeout(function() {document.getElementById('${figAireCorr2.id}').style.visibility = \"visible'}, 5000),document.getElementById('translat${q}\").beginElement()\"><i class=\"redo circle icon\"></i>Restart area comparison animation </button>`\n            }\n          }\n          // Interactive MCQ\n          if (this.interactif) {\n            reponsePerimetre2 = true\n            reponseAire1 = !aleaDemiDisque\n            reponseAire2 = aleaDemiDisque\n          }\n          break\n        case 5: // Deux demi-disques en plus\n          E = point(entreDeux(A.x, A.x + (B.x - A.x) / 3), A.y)\n          F = point(entreDeux(B.x, A.x + 2 * (B.x - A.x) / 3), A.y)\n          G = point(B.x, entreDeux(B.y, B.y + (C.y - B.y) / 3))\n          H = point(B.x, entreDeux(C.y, B.y + 2 * (C.y - B.y) / 3))\n          I = point(entreDeux(B.x, A.x + 2 * (B.x - A.x) / 3), D.y)\n          J = point(entreDeux(A.x, A.x + (B.x - A.x) / 3), D.y)\n          K = point(A.x, entreDeux(C.y, B.y + 2 * (C.y - B.y) / 3))\n          L = point(A.x, entreDeux(B.y, B.y + (C.y - B.y) / 3))\n          poly = polygone(A, B, C, D)\n          poly.couleurDeRemplissage = colorToLatexOrHTML(color[q])\n          poly.opaciteDeRemplissage = 0.5\n          poly.color = 'none'\n          objets.push(poly)\n          rayonOuCote = arrondi((min(longueur(E, F), longueur(G, H), longueur(I, J), longueur(K, L))) / 2)\n          M = translation(E, vecteur(rayonOuCote, 0))\n          N = translation(G, vecteur(0, rayonOuCote))\n          O = translation(I, vecteur(-rayonOuCote, 0))\n          P = translation(K, vecteur(0, -rayonOuCote))\n          paramsEnonce = { xmin: -0.5, ymin: -0.5, xmax: B.x + 0.5, ymax: C.y + 0.5, pixelsParCm: 30, scale: 0.7, mainlevee: false }\n          choixFig = randint(0, 3)\n          switch (choixFig) {\n            case 0:\n              pt1 = M\n              pt2 = E\n              paramsEnonce.ymin = -0.5 - rayonOuCote\n              break\n            case 1:\n              pt1 = N\n              pt2 = G\n              paramsEnonce.xmax = rayonOuCote + B.x + 0.5\n              break\n            case 2:\n              pt1 = O\n              pt2 = I\n              paramsEnonce.ymax = rayonOuCote + C.y + 0.5\n              break\n            case 3:\n              pt1 = P\n              pt2 = K\n              paramsEnonce.xmin = -0.5 - rayonOuCote\n              break\n          }\n          figAire1 = arc(pt2, pt1, 180, false, color[q], 'black', 0.5)\n          choixFig2 = randint(0, 3, [choixFig])\n          choixFigAire2 = [\n            [E, M],\n            [G, N],\n            [I, O],\n            [K, P]\n          ]\n          paramsEnonce.ymin = choixFig2 === 0 ? -0.5 - rayonOuCote : paramsEnonce.ymin\n          paramsEnonce.xmax = choixFig2 === 1 ? rayonOuCote + B.x + 0.5 : paramsEnonce.xmax\n          paramsEnonce.ymax = choixFig2 === 2 ? rayonOuCote + C.y + 0.5 : paramsEnonce.ymax\n          paramsEnonce.xmin = choixFig2 === 3 ? -0.5 - rayonOuCote : paramsEnonce.xmin\n\n          figAire2 = arc(choixFigAire2[choixFig2][0], choixFigAire2[choixFig2][1], 180, false, color[q], 'black', 0.5)\n          M = rotation(pt2, pt1, 60)\n          N = segment(M, pt1, 'black')\n          N.epaisseur = 2\n          O = rotation(choixFigAire2[choixFig2][0], choixFigAire2[choixFig2][1], 60)\n          P = segment(O, choixFigAire2[choixFig2][1], 'black')\n          P.epaisseur = 2\n          objets.push(figAire1, figAire2, N, codageSegment(M, pt1, '|||'), P, codageSegment(O, choixFigAire2[choixFig2][1], '|||'), rect)\n          texte = mathalea2d(paramsEnonce, objets)\n          // Correction\n          texteCorr = (this.sup2 === 3) ? numAlpha(0) : ''\n          texteCorr += (this.sup2 === 1 || this.sup2 === 3 || aireOuPerimetre !== 'Area') ? 'You have to cover more ground to go around the colored figure than around the hatched rectangle. Therefore, the colored figure has a larger perimeter than that of the hatched rectangle.' : ''\n          texteCorr += (this.sup2 === 3) ? '<br>' + numAlpha(1) : ''\n          texteCorr += (this.sup2 === 2 || this.sup2 === 3 || aireOuPerimetre !== 'Perimeter') ? 'The hatched rectangle covers less area than the colored figure. Therefore, the colored figure has an area greater than that of the hatched rectangle.' : ''\n          // Interactive MCQ\n          if (this.interactif) {\n            reponsePerimetre2 = true\n            reponseAire2 = true\n          }\n          break\n        case 6: // Deux demi-disques en moins\n          E = point(entreDeux(A.x, A.x + (B.x - A.x) / 3), A.y)\n          F = point(entreDeux(B.x, A.x + 2 * (B.x - A.x) / 3), A.y)\n          G = point(B.x, entreDeux(B.y, B.y + (C.y - B.y) / 3))\n          H = point(B.x, entreDeux(C.y, B.y + 2 * (C.y - B.y) / 3))\n          I = point(entreDeux(B.x, A.x + 2 * (B.x - A.x) / 3), D.y)\n          J = point(entreDeux(A.x, A.x + (B.x - A.x) / 3), D.y)\n          K = point(A.x, entreDeux(C.y, B.y + 2 * (C.y - B.y) / 3))\n          L = point(A.x, entreDeux(B.y, B.y + (C.y - B.y) / 3))\n          poly = polygone(A, B, C, D)\n          poly.couleurDeRemplissage = colorToLatexOrHTML(color[q])\n          poly.opaciteDeRemplissage = 0.5\n          poly.color = 'none'\n          objets.push(poly)\n          rayonOuCote = arrondi((min(longueur(E, F), longueur(G, H), longueur(I, J), longueur(K, L))) / 2)\n          M = translation(E, vecteur(rayonOuCote, 0))\n          N = translation(G, vecteur(0, rayonOuCote))\n          O = translation(I, vecteur(-rayonOuCote, 0))\n          P = translation(K, vecteur(0, -rayonOuCote))\n          paramsEnonce = { xmin: -0.5, ymin: -0.5, xmax: B.x + 0.5, ymax: C.y + 0.5, pixelsParCm: 30, scale: 0.7, mainlevee: false }\n          choixFig = randint(0, 3)\n          switch (choixFig) {\n            case 0:\n              pt1 = M\n              pt2 = E\n              paramsEnonce.ymin = -0.5 - rayonOuCote\n              break\n            case 1:\n              pt1 = N\n              pt2 = G\n              paramsEnonce.xmax = rayonOuCote + B.x + 0.5\n              break\n            case 2:\n              pt1 = O\n              pt2 = I\n              paramsEnonce.ymax = rayonOuCote + C.y + 0.5\n              break\n            case 3:\n              pt1 = P\n              pt2 = K\n              paramsEnonce.xmin = -0.5 - rayonOuCote\n              break\n          }\n          figAire1 = arc(pt2, pt1, -180, false, 'white', 'black', 1.1)\n          choixFig2 = randint(0, 3, [choixFig])\n          choixFigAire2 = [\n            [E, M],\n            [G, N],\n            [I, O],\n            [K, P]\n          ]\n          paramsEnonce.ymin = choixFig2 === 0 ? -0.5 - rayonOuCote : paramsEnonce.ymin\n          paramsEnonce.xmax = choixFig2 === 1 ? rayonOuCote + B.x + 0.5 : paramsEnonce.xmax\n          paramsEnonce.ymax = choixFig2 === 2 ? rayonOuCote + C.y + 0.5 : paramsEnonce.ymax\n          paramsEnonce.xmin = choixFig2 === 3 ? -0.5 - rayonOuCote : paramsEnonce.xmin\n\n          figAire2 = arc(choixFigAire2[choixFig2][0], choixFigAire2[choixFig2][1], -180, false, 'white', 'black', 1.1)\n          M = rotation(pt2, pt1, -60)\n          N = segment(M, pt1, 'black')\n          N.epaisseur = 2\n          O = rotation(choixFigAire2[choixFig2][0], choixFigAire2[choixFig2][1], -60)\n          P = segment(O, choixFigAire2[choixFig2][1], 'black')\n          P.epaisseur = 2\n          objets.push(figAire1, figAire2, N, codageSegment(M, pt1, '|||'), P, codageSegment(O, choixFigAire2[choixFig2][1], '|||'), rect)\n          texte = mathalea2d(paramsEnonce, objets)\n          // Correction\n          texteCorr = (this.sup2 === 3) ? numAlpha(0) : ''\n          texteCorr += (this.sup2 === 1 || this.sup2 === 3 || aireOuPerimetre !== 'Area') ? 'You have to cover more ground to go around the colored figure than around the hatched rectangle. Therefore, the colored figure has a larger perimeter than that of the hatched rectangle.' : ''\n          texteCorr += (this.sup2 === 3) ? '<br>' + numAlpha(1) : ''\n          texteCorr += (this.sup2 === 2 || this.sup2 === 3 || aireOuPerimetre !== 'Perimeter') ? 'The hatched rectangle covers more area than the colored figure. Therefore, the hatched rectangle has an area greater than that of the colored figure.' : ''\n          // Interactive MCQ\n          if (this.interactif) {\n            reponsePerimetre2 = true\n            reponseAire1 = true\n          }\n          break\n        case 7: // Un quadrilatère inscrit dans le rectangle\n          E = point(entreDeux(A.x, B.x), A.y)\n          F = point(B.x, entreDeux(B.y, C.y))\n          G = point(entreDeux(A.x, B.x), C.y)\n          H = point(A.x, entreDeux(B.y, C.y))\n          poly = polygone(E, F, G, H)\n          poly.couleurDeRemplissage = colorToLatexOrHTML(color[q])\n          poly.opaciteDeRemplissage = 0.5\n          objets.push(poly, rect)\n          paramsEnonce = { xmin: -0.5, ymin: -0.5, xmax: B.x + 0.5, ymax: C.y + 0.5, pixelsParCm: 30, scale: 0.7, mainlevee: false }\n          texte = mathalea2d(paramsEnonce, objets)\n          // Correction\n          texteCorr = (this.sup2 === 3) ? numAlpha(0) : ''\n          texteCorr += (this.sup2 === 1 || this.sup2 === 3 || aireOuPerimetre !== 'Area') ? 'You have to cover less distance to go around the colored figure than around the hatched rectangle. Therefore, the hatched rectangle has a larger perimeter than that of the colored figure.' : ''\n          texteCorr += (this.sup2 === 3) ? '<br>' + numAlpha(1) : ''\n          texteCorr += (this.sup2 === 2 || this.sup2 === 3 || aireOuPerimetre !== 'Perimeter') ? 'The hatched rectangle covers more area than the colored figure. Therefore, the hatched rectangle has an area greater than that of the colored figure.' : ''\n          // Interactive MCQ\n          if (this.interactif) {\n            reponsePerimetre1 = true\n            reponseAire1 = true\n          }\n          break\n        case 8: // Le rectangle inscrit dans un quadrilatère\n          aleaPente = choice([0, 0.5])\n          d1 = droiteParPointEtPente(A, -(aleaPente + randint(10, 50) / 100))\n          d2 = droiteParPointEtPente(B, -(aleaPente - randint(50, 90) / 100))\n          d3 = droiteParPointEtPente(C, -(aleaPente + randint(10, 50) / 100))\n          d4 = droiteParPointEtPente(D, -(aleaPente - randint(50, 90) / 100))\n          E = pointIntersectionDD(d1, d2)\n          F = pointIntersectionDD(d2, d3)\n          G = pointIntersectionDD(d3, d4)\n          H = pointIntersectionDD(d4, d1)\n          poly = polygone(E, F, G, H)\n          poly.couleurDeRemplissage = colorToLatexOrHTML(color[q])\n          poly.opaciteDeRemplissage = 0.5\n          objets.push(poly, rect)\n          paramsEnonce = { xmin: H.x - 0.5, ymin: E.y - 0.5, xmax: F.x + 0.5, ymax: G.y + 0.5, pixelsParCm: 30, scale: 0.7, mainlevee: false }\n          texte = mathalea2d(paramsEnonce, objets)\n          // Correction\n          texteCorr = (this.sup2 === 3) ? numAlpha(0) : ''\n          texteCorr += (this.sup2 === 1 || this.sup2 === 3 || aireOuPerimetre !== 'Area') ? 'You have to cover more ground to go around the colored figure than around the hatched rectangle. Therefore, the colored figure has a larger perimeter than that of the hatched rectangle.' : ''\n          texteCorr += (this.sup2 === 3) ? '<br>' + numAlpha(1) : ''\n          texteCorr += (this.sup2 === 2 || this.sup2 === 3 || aireOuPerimetre !== 'Perimeter') ? 'The hatched rectangle covers less area than the colored figure. Therefore, the colored figure has an area greater than that of the hatched rectangle.' : ''\n          // Interactive MCQ\n          if (this.interactif) {\n            reponsePerimetre2 = true\n            reponseAire2 = true\n          }\n          break\n        case 9: // Deux triangles alternés qui s'emboîtent\n          E = point(entreDeux(A.x, A.x + (B.x - A.x) / 3), A.y)\n          F = point(entreDeux(B.x, A.x + 2 * (B.x - A.x) / 3), A.y)\n          G = point(B.x, entreDeux(B.y, B.y + (C.y - B.y) / 3))\n          H = point(B.x, entreDeux(C.y, B.y + 2 * (C.y - B.y) / 3))\n          I = point(entreDeux(B.x, A.x + 2 * (B.x - A.x) / 3), D.y)\n          J = point(entreDeux(A.x, A.x + (B.x - A.x) / 3), D.y)\n          K = point(A.x, entreDeux(C.y, B.y + 2 * (C.y - B.y) / 3))\n          L = point(A.x, entreDeux(B.y, B.y + (C.y - B.y) / 3))\n          poly = polygone(A, B, C, D)\n          poly.couleurDeRemplissage = colorToLatexOrHTML(color[q])\n          poly.opaciteDeRemplissage = 0.5\n          poly.color = 'none'\n          objets.push(poly)\n          rayonOuCote = (min(longueur(E, F), longueur(G, H), longueur(I, J), longueur(K, L)))\n          M = translation(E, vecteur(rayonOuCote, 0))\n          N = translation(G, vecteur(0, rayonOuCote))\n          O = translation(I, vecteur(-rayonOuCote, 0))\n          P = translation(K, vecteur(0, -rayonOuCote))\n          paramsEnonce = { xmin: -0.5, ymin: -0.5, xmax: B.x + 0.5, ymax: C.y + 0.5, pixelsParCm: 30, scale: 0.7, mainlevee: false }\n          aleaLongueur = choice([-1, 1])\n          choixFig = randint(0, 3)\n          switch (choixFig) {\n            case 0:\n              pt1 = M\n              pt2 = E\n              paramsEnonce.ymin = -0.5 - rayonOuCote - aleaLongueur\n              break\n            case 1:\n              pt1 = N\n              pt2 = G\n              paramsEnonce.xmax = rayonOuCote + aleaLongueur + B.x + 0.5\n              break\n            case 2:\n              pt1 = O\n              pt2 = I\n              paramsEnonce.ymax = rayonOuCote + aleaLongueur + C.y + 0.5\n              break\n            case 3:\n              pt1 = P\n              pt2 = K\n              paramsEnonce.xmin = -0.5 - rayonOuCote - aleaLongueur\n              break\n          }\n          aleaAngle = choice([40, 50, 70, 80])\n          Q = pointSurSegment(pt2, pt1, rayonOuCote + aleaLongueur)\n          R = rotation(Q, pt2, -aleaAngle)\n          figAire1 = polygone(pt2, pt1, R)\n          figAire1.color = 'none'\n          figAire1.couleurDeRemplissage = colorToLatexOrHTML(color[q])\n          figAire1.opaciteDeRemplissage = 0.5\n          choixFig2 = randint(0, 3, [choixFig])\n          choixFigAire2 = [\n            [E, M],\n            [G, N],\n            [I, O],\n            [K, P]\n          ]\n          paramsEnonce.xmax = choixFig2 === 1 ? rayonOuCote + B.x + 0.5 : paramsEnonce.xmax\n          paramsEnonce.xmin = choixFig2 === 3 ? -0.5 - rayonOuCote : paramsEnonce.xmin\n          S = pointSurSegment(choixFigAire2[choixFig2][1], choixFigAire2[choixFig2][0], rayonOuCote + aleaLongueur)\n          T = rotation(S, choixFigAire2[choixFig2][1], -aleaAngle)\n          figAire2 = polygone(choixFigAire2[choixFig2][0], choixFigAire2[choixFig2][1], T)\n          figAire2.color = 'none'\n          figAire2.couleurDeRemplissage = colorToLatexOrHTML('white')\n          figAire2.opaciteDeRemplissage = 1.1\n          objets.push(figAire1, figAire2, segment(pt2, R), segment(pt1, R), codageSegment(pt2, R, '|||'), codageSegment(pt2, pt1, 'OO'), codageSegment(pt1, R, 'XX'), rect)\n          objets.push(segment(choixFigAire2[choixFig2][0], T), segment(choixFigAire2[choixFig2][1], T), codageSegment(choixFigAire2[choixFig2][1], T, '|||'), codageSegment(choixFigAire2[choixFig2][1], choixFigAire2[choixFig2][0], 'OO'), codageSegment(choixFigAire2[choixFig2][0], T, 'XX'))\n          texte = mathalea2d(paramsEnonce, objets)\n          // Correction\n          texteCorr = (this.sup2 === 3) ? numAlpha(0) : ''\n          texteCorr += (this.sup2 === 1 || this.sup2 === 3 || aireOuPerimetre !== 'Area') ? 'You have to cover more ground to go around the colored figure than around the hatched rectangle. Therefore, the colored figure has a larger perimeter than that of the hatched rectangle.' : ''\n          texteCorr += (this.sup2 === 3) ? '<br>' + numAlpha(1) : ''\n          texteCorr += (this.sup2 === 2 || this.sup2 === 3 || aireOuPerimetre !== 'Perimeter') ? 'The hatched rectangle covers as much surface as the colored figure. Therefore, the colored figure has an area equal to that of the hatched rectangle.' : ''\n          objets = []\n          if ((this.sup2 === 2 || this.sup2 === 3 || aireOuPerimetre !== 'Perimeter')) {\n            figAire1 = polygone(pt2, pt1, R)\n            figAire1.color = 'none'\n            figAire1.couleurDeRemplissage = colorToLatexOrHTML('white')\n            figAire1.opaciteDeRemplissage = 1.1\n            figAireCorr = polygone(pt2, pt1, R)\n            figAireCorr.couleurDeRemplissage = colorToLatexOrHTML(color[q])\n            figAireCorr.opaciteDeRemplissage = 0.5\n            angleCorr = choixFig2 - choixFig < 0 ? choixFig2 - choixFig + 4 : choixFig2 - choixFig\n            angleCorr = angleCorr === 1 ? 90 : angleCorr === 2 ? 0 : -90\n            figAireCorr2 = rotation(figAire2, choixFigAire2[choixFig2][0], angleCorr)\n            figAireCorr2.couleurDeRemplissage = colorToLatexOrHTML(color[q])\n            figAireCorr2.opaciteDeRemplissage = 0.5\n            objets.push(poly, figAire1, figAire2, segment(pt2, R), segment(pt1, R), codageSegment(pt2, R, '|||'), codageSegment(pt2, pt1, 'OO'), codageSegment(pt1, R, 'XX'), rect)\n            objets.push(segment(choixFigAire2[choixFig2][0], T), segment(choixFigAire2[choixFig2][1], T), codageSegment(choixFigAire2[choixFig2][1], T, '|||'), codageSegment(choixFigAire2[choixFig2][1], choixFigAire2[choixFig2][0], 'OO'), codageSegment(choixFigAire2[choixFig2][0], T, 'XX'))\n            objets.push(translationPuisRotationAnimees(q, figAireCorr, vecteur(pt1, choixFigAire2[choixFig2][0]), figAireCorr2, choixFigAire2[choixFig2][0], -angleCorr))\n            paramsEnonce.ymin = choixFig2 === 0 ? -0.5 - rayonOuCote : paramsEnonce.ymin\n            paramsEnonce.ymax = choixFig2 === 2 ? rayonOuCote + C.y + 0.5 : paramsEnonce.ymax\n            texteCorr += '<br>' + mathalea2d(paramsEnonce, objets)\n            if (context.isHtml) {\n              texteCorr += `<br><button class='btn ui labeled icon button'  style='margin:10px' onclick=\"document.getElementById('${figAireCorr.id}').style.visibility = 'visible',document.getElementById('${figAireCorr2.id}').style.visibility = 'hidden',\n              setTimeout(function() {document.getElementById('${figAireCorr.id}').style.visibility = 'hidden'}, 5000),\n              setTimeout(function() {document.getElementById('${figAireCorr2.id}').style.visibility = \"visible'}, 5000),document.getElementById('translat${q}\").beginElement()\"><i class=\"redo circle icon\"></i>Restart area comparison animation </button>`\n            }\n          }\n          // Interactive MCQ\n          if (this.interactif) {\n            reponsePerimetre2 = true\n            reponseAire3 = true\n          }\n          break\n        case 10: // Deux triangles alternés qui ne s'emboîtent pas\n          E = point(entreDeux(A.x, A.x + (B.x - A.x) / 3), A.y)\n          F = point(entreDeux(B.x, A.x + 2 * (B.x - A.x) / 3), A.y)\n          G = point(B.x, entreDeux(B.y, B.y + (C.y - B.y) / 3))\n          H = point(B.x, entreDeux(C.y, B.y + 2 * (C.y - B.y) / 3))\n          I = point(entreDeux(B.x, A.x + 2 * (B.x - A.x) / 3), D.y)\n          J = point(entreDeux(A.x, A.x + (B.x - A.x) / 3), D.y)\n          K = point(A.x, entreDeux(C.y, B.y + 2 * (C.y - B.y) / 3))\n          L = point(A.x, entreDeux(B.y, B.y + (C.y - B.y) / 3))\n          poly = polygone(A, B, C, D)\n          poly.couleurDeRemplissage = colorToLatexOrHTML(color[q])\n          poly.opaciteDeRemplissage = 0.5\n          poly.color = 'none'\n          objets.push(poly)\n          rayonOuCote = (min(longueur(E, F), longueur(G, H), longueur(I, J), longueur(K, L)))\n          M = translation(E, vecteur(rayonOuCote, 0))\n          N = translation(G, vecteur(0, rayonOuCote))\n          O = translation(I, vecteur(-rayonOuCote, 0))\n          P = translation(K, vecteur(0, -rayonOuCote))\n          paramsEnonce = { xmin: -0.5, ymin: -0.5, xmax: B.x + 0.5, ymax: C.y + 0.5, pixelsParCm: 30, scale: 0.7, mainlevee: false }\n          aleaLongueur = choice([-1, 1])\n          choixFig = randint(0, 3)\n          switch (choixFig) {\n            case 0:\n              pt1 = M\n              pt2 = E\n              paramsEnonce.ymin = -0.5 - rayonOuCote - aleaLongueur\n              break\n            case 1:\n              pt1 = N\n              pt2 = G\n              paramsEnonce.xmax = rayonOuCote + aleaLongueur + B.x + 0.5\n              break\n            case 2:\n              pt1 = O\n              pt2 = I\n              paramsEnonce.ymax = rayonOuCote + aleaLongueur + C.y + 0.5\n              break\n            case 3:\n              pt1 = P\n              pt2 = K\n              paramsEnonce.xmin = -0.5 - rayonOuCote - aleaLongueur\n              break\n          }\n          aleaAngle = choice([40, 50, 70, 80])\n          Q = pointSurSegment(pt2, pt1, rayonOuCote + aleaLongueur)\n          R = rotation(Q, pt2, -aleaAngle)\n          figAire1 = polygone(pt2, pt1, R)\n          figAire1.color = 'none'\n          figAire1.couleurDeRemplissage = colorToLatexOrHTML(color[q])\n          figAire1.opaciteDeRemplissage = 0.5\n          choixFig2 = randint(0, 3, [choixFig])\n          hauteur = longueur(R, projectionOrtho(R, droite(pt1, pt2))) // Longueur de la hauteur issue de R dans figAire1\n          choixFigAire2 = [\n            [E, M, arrondi(min(hauteur / longueur(B, C), longueur(E, B) / longueur(E, M)))], // Le dernier nombre est le rapport homothétique maximal pour ne pas que le triangle sorte du triangle.\n            [G, N, arrondi(min(hauteur / longueur(A, B), longueur(G, C) / longueur(G, N)))],\n            [I, O, arrondi(min(hauteur / longueur(B, C), longueur(I, D) / longueur(I, O)))],\n            [K, P, arrondi(min(hauteur / longueur(A, B), longueur(K, A) / longueur(K, P)))]\n          ]\n          if (choixFig2 === 1) paramsEnonce.xmax = rayonOuCote + B.x + 0.5\n          if (choixFig2 === 3) paramsEnonce.xmin = -0.5 - rayonOuCote\n          S = pointSurSegment(choixFigAire2[choixFig2][1], choixFigAire2[choixFig2][0], rayonOuCote + aleaLongueur)\n          T = rotation(S, choixFigAire2[choixFig2][1], -aleaAngle)\n          figAire2 = polygone(choixFigAire2[choixFig2][0], choixFigAire2[choixFig2][1], T)\n          aleaRapportHomothetie = choice([0.7, 0.8, arrondi(min(1.2, choixFigAire2[choixFig2][2] - 0.01)), min(1.3, arrondi(choixFigAire2[choixFig2][2] - 0.01))])\n          figAire2 = homothetie(figAire2, choixFigAire2[choixFig2][0], aleaRapportHomothetie)\n          figAire2.color = 'none'\n          figAire2.couleurDeRemplissage = colorToLatexOrHTML('white')\n          figAire2.opaciteDeRemplissage = 1.1\n          objets.push(figAire1, figAire2, segment(pt2, R), segment(pt1, R), rect)\n          objets.push(homothetie(segment(choixFigAire2[choixFig2][0], T), choixFigAire2[choixFig2][0], aleaRapportHomothetie), homothetie(segment(choixFigAire2[choixFig2][1], T), choixFigAire2[choixFig2][0], aleaRapportHomothetie))\n          texte = mathalea2d(paramsEnonce, objets)\n          // Correction\n          texteCorr = (this.sup2 === 3) ? numAlpha(0) : ''\n          texteCorr += (this.sup2 === 1 || this.sup2 === 3 || aireOuPerimetre !== 'Area') ? 'You have to cover more ground to go around the colored figure than around the hatched rectangle. Therefore, the colored figure has a larger perimeter than that of the hatched rectangle.' : ''\n          texteCorr += (this.sup2 === 3) ? '<br>' + numAlpha(1) : ''\n          texteCorr += aleaRapportHomothetie < 1\n            ? ((this.sup2 === 2 || this.sup2 === 3 || aireOuPerimetre !== 'Perimeter') ? 'The hatched rectangle covers less area than the colored figure. Therefore, the colored figure has an area greater than that of the hatched rectangle.' : '')\n            : ((this.sup2 === 2 || this.sup2 === 3 || aireOuPerimetre !== 'Perimeter') ? 'The hatched rectangle covers more area than the colored figure. Therefore, the hatched rectangle has an area greater than that of the colored figure.' : '')\n          if ((this.sup2 === 2 || this.sup2 === 3 || aireOuPerimetre !== 'Perimeter')) {\n            objets = []\n            figAire1 = polygone(pt2, pt1, R)\n            figAire1.color = 'none'\n            figAire1.couleurDeRemplissage = colorToLatexOrHTML('white')\n            figAire1.opaciteDeRemplissage = 1.1\n            figAireCorr = polygone(pt2, pt1, R)\n            figAireCorr.couleurDeRemplissage = colorToLatexOrHTML(color[q])\n            figAireCorr.opaciteDeRemplissage = 0.5\n            figAire2Corr = homothetie(figAire2, choixFigAire2[choixFig2][0], 1 / aleaRapportHomothetie)\n            angleCorr = choixFig2 - choixFig < 0 ? choixFig2 - choixFig + 4 : choixFig2 - choixFig\n            angleCorr = angleCorr === 1 ? 90 : angleCorr === 2 ? 0 : -90\n            figAireCorr2 = rotation(figAire2Corr, choixFigAire2[choixFig2][0], angleCorr)\n            figAireCorr2.couleurDeRemplissage = colorToLatexOrHTML(color[q])\n            figAireCorr2.opaciteDeRemplissage = 0.5\n            objets.push(poly, figAire1, figAire2, segment(pt2, R), segment(pt1, R), rect)\n            objets.push(homothetie(segment(choixFigAire2[choixFig2][0], T), choixFigAire2[choixFig2][0], aleaRapportHomothetie), homothetie(segment(choixFigAire2[choixFig2][1], T), choixFigAire2[choixFig2][0], aleaRapportHomothetie))\n            objets.push(translationPuisRotationAnimees(q, figAireCorr, vecteur(pt1, choixFigAire2[choixFig2][0]), figAireCorr2, choixFigAire2[choixFig2][0], -angleCorr))\n            paramsEnonce.ymin = choixFig2 === 0 ? -0.5 - rayonOuCote : paramsEnonce.ymin\n            paramsEnonce.ymax = choixFig2 === 2 ? rayonOuCote + C.y + 0.5 : paramsEnonce.ymax\n            texteCorr += '<br>' + mathalea2d(paramsEnonce, objets)\n            if (context.isHtml) {\n              texteCorr += `<br><button class='btn ui labeled icon button'  style='margin:10px' onclick=\"document.getElementById('${figAireCorr.id}').style.visibility = 'visible',document.getElementById('${figAireCorr2.id}').style.visibility = 'hidden',\n              setTimeout(function() {document.getElementById('${figAireCorr.id}').style.visibility = 'hidden'}, 5000),\n              setTimeout(function() {document.getElementById('${figAireCorr2.id}').style.visibility = \"visible'}, 5000),document.getElementById('translat${q}\").beginElement()\"><i class=\"redo circle icon\"></i>Restart area comparison animation </button>`\n            }\n          }\n          // Interactive MCQ\n          if (this.interactif) {\n            reponsePerimetre2 = true\n            reponseAire1 = !(aleaRapportHomothetie < 1)\n            reponseAire2 = aleaRapportHomothetie < 1\n          }\n          break\n        case 11: // Deux triangles en plus\n          E = point(entreDeux(A.x, A.x + (B.x - A.x) / 3), A.y)\n          F = point(entreDeux(B.x, A.x + 2 * (B.x - A.x) / 3), A.y)\n          G = point(B.x, entreDeux(B.y, B.y + (C.y - B.y) / 3))\n          H = point(B.x, entreDeux(C.y, B.y + 2 * (C.y - B.y) / 3))\n          I = point(entreDeux(B.x, A.x + 2 * (B.x - A.x) / 3), D.y)\n          J = point(entreDeux(A.x, A.x + (B.x - A.x) / 3), D.y)\n          K = point(A.x, entreDeux(C.y, B.y + 2 * (C.y - B.y) / 3))\n          L = point(A.x, entreDeux(B.y, B.y + (C.y - B.y) / 3))\n          poly = polygone(A, B, C, D)\n          poly.couleurDeRemplissage = colorToLatexOrHTML(color[q])\n          poly.opaciteDeRemplissage = 0.5\n          poly.color = 'none'\n          objets.push(poly)\n          rayonOuCote = (min(longueur(E, F), longueur(G, H), longueur(I, J), longueur(K, L)))\n          M = translation(E, vecteur(rayonOuCote, 0))\n          N = translation(G, vecteur(0, rayonOuCote))\n          O = translation(I, vecteur(-rayonOuCote, 0))\n          P = translation(K, vecteur(0, -rayonOuCote))\n          paramsEnonce = { xmin: -0.5, ymin: -0.5, xmax: B.x + 0.5, ymax: C.y + 0.5, pixelsParCm: 30, scale: 0.7, mainlevee: false }\n          aleaLongueur = choice([-1, 1])\n          choixFig = randint(0, 3)\n          switch (choixFig) {\n            case 0:\n              pt1 = M\n              pt2 = E\n              paramsEnonce.ymin = -0.5 - rayonOuCote - aleaLongueur\n              break\n            case 1:\n              pt1 = N\n              pt2 = G\n              paramsEnonce.xmax = rayonOuCote + aleaLongueur + B.x + 0.5\n              break\n            case 2:\n              pt1 = O\n              pt2 = I\n              paramsEnonce.ymax = rayonOuCote + aleaLongueur + C.y + 0.5\n              break\n            case 3:\n              pt1 = P\n              pt2 = K\n              paramsEnonce.xmin = -0.5 - rayonOuCote - aleaLongueur\n              break\n          }\n          aleaAngle = choice([40, 50, 70, 80, 100, 110])\n          Q = pointSurSegment(pt2, pt1, rayonOuCote + aleaLongueur)\n          R = rotation(Q, pt2, -aleaAngle)\n          switch (choixFig) {\n            case 0:\n            case 2:\n              paramsEnonce.xmin = -0.5 + min(A.x, R.x)\n              paramsEnonce.xmax = 0.5 + max(B.x, R.x)\n              break\n            case 1 :\n            case 3 :\n              paramsEnonce.ymin = -0.5 + min(A.y, R.y)\n              paramsEnonce.ymax = 0.5 + max(D.y, R.y)\n              break\n          }\n          figAire1 = polygone(pt2, pt1, R)\n          figAire1.color = 'none'\n          figAire1.couleurDeRemplissage = colorToLatexOrHTML(color[q])\n          figAire1.opaciteDeRemplissage = 0.5\n          choixFig2 = randint(0, 3, [choixFig])\n          choixFigAire2 = [\n            [E, M],\n            [G, N],\n            [I, O],\n            [K, P]\n          ]\n          S = pointSurSegment(choixFigAire2[choixFig2][1], choixFigAire2[choixFig2][0], rayonOuCote + aleaLongueur)\n          T = rotation(S, choixFigAire2[choixFig2][1], aleaAngle)\n          switch (choixFig2) {\n            case 0 :\n              paramsEnonce.xmin = -0.5 + min(A.x, T.x, R.x)\n              paramsEnonce.xmax = 0.5 + max(B.x, T.x, R.x)\n              paramsEnonce.ymin = -0.5 - rayonOuCote - aleaLongueur\n              break\n            case 1 :\n              paramsEnonce.ymin = -0.5 + min(A.y, T.y, R.y)\n              paramsEnonce.ymax = 0.5 + max(D.y, T.y, R.y)\n              paramsEnonce.xmax = rayonOuCote + aleaLongueur + B.x + 0.5\n              break\n            case 2 :\n              paramsEnonce.xmin = -0.5 + min(A.x, T.x, R.x)\n              paramsEnonce.xmax = 0.5 + max(B.x, T.x, R.x)\n              paramsEnonce.ymax = rayonOuCote + aleaLongueur + C.y + 0.5\n              break\n            case 3 :\n              paramsEnonce.ymin = -0.5 + min(A.y, T.y, R.y)\n              paramsEnonce.ymax = 0.5 + max(D.y, T.y, R.y)\n              paramsEnonce.xmin = -0.5 - rayonOuCote - aleaLongueur\n              break\n          }\n          figAire2 = polygone(choixFigAire2[choixFig2][0], choixFigAire2[choixFig2][1], T)\n          figAire2.color = 'none'\n          figAire2.couleurDeRemplissage = colorToLatexOrHTML(color[q])\n          figAire2.opaciteDeRemplissage = 0.5\n          objets.push(figAire1, figAire2, segment(pt2, R), segment(pt1, R), codageSegment(pt2, R, '|||'), codageSegment(pt2, pt1, 'OO'), codageSegment(pt1, R, 'XX'), rect)\n          objets.push(segment(choixFigAire2[choixFig2][0], T), segment(choixFigAire2[choixFig2][1], T), codageSegment(choixFigAire2[choixFig2][1], T, '|||'), codageSegment(choixFigAire2[choixFig2][1], choixFigAire2[choixFig2][0], 'OO'), codageSegment(choixFigAire2[choixFig2][0], T, 'XX'))\n          texte = mathalea2d(paramsEnonce, objets)\n          // Correction\n          texteCorr = (this.sup2 === 3) ? numAlpha(0) : ''\n          texteCorr += (this.sup2 === 1 || this.sup2 === 3 || aireOuPerimetre !== 'Area') ? 'You have to cover more ground to go around the colored figure than around the hatched rectangle. Therefore, the colored figure has a larger perimeter than that of the hatched rectangle.' : ''\n          texteCorr += (this.sup2 === 3) ? '<br>' + numAlpha(1) : ''\n          texteCorr += (this.sup2 === 2 || this.sup2 === 3 || aireOuPerimetre !== 'Perimeter') ? 'The hatched rectangle covers less area than the colored figure. Therefore, the colored figure has an area greater than that of the hatched rectangle.' : ''\n          // Interactive MCQ\n          if (this.interactif) {\n            reponsePerimetre2 = true\n            reponseAire2 = true\n          }\n          break\n        case 12: // Deux triangles en moins\n          E = point(entreDeux(A.x, A.x + (B.x - A.x) / 3), A.y)\n          F = point(entreDeux(B.x, A.x + 2 * (B.x - A.x) / 3), A.y)\n          G = point(B.x, entreDeux(B.y, B.y + (C.y - B.y) / 3))\n          H = point(B.x, entreDeux(C.y, B.y + 2 * (C.y - B.y) / 3))\n          I = point(entreDeux(B.x, A.x + 2 * (B.x - A.x) / 3), D.y)\n          J = point(entreDeux(A.x, A.x + (B.x - A.x) / 3), D.y)\n          K = point(A.x, entreDeux(C.y, B.y + 2 * (C.y - B.y) / 3))\n          L = point(A.x, entreDeux(B.y, B.y + (C.y - B.y) / 3))\n          poly = polygone(A, B, C, D)\n          poly.couleurDeRemplissage = colorToLatexOrHTML(color[q])\n          poly.opaciteDeRemplissage = 1.1\n          poly.color = 'none'\n          objets.push(poly)\n          rayonOuCote = (min(longueur(E, F), longueur(G, H), longueur(I, J), longueur(K, L)))\n          M = translation(E, vecteur(rayonOuCote, 0))\n          N = translation(G, vecteur(0, rayonOuCote))\n          O = translation(I, vecteur(-rayonOuCote, 0))\n          P = translation(K, vecteur(0, -rayonOuCote))\n          paramsEnonce = { xmin: -0.5, ymin: -0.5, xmax: B.x + 0.5, ymax: C.y + 0.5, pixelsParCm: 30, scale: 0.7, mainlevee: false }\n          aleaLongueur = -1\n          choixFig = randint(0, 3)\n          switch (choixFig) {\n            case 0:\n              pt1 = M\n              pt2 = E\n              break\n            case 1:\n              pt1 = N\n              pt2 = G\n              break\n            case 2:\n              pt1 = O\n              pt2 = I\n              break\n            case 3:\n              pt1 = P\n              pt2 = K\n              break\n          }\n          aleaAngle = choice([40, 50, 70, 80, 100, 110])\n          Q = pointSurSegment(pt2, pt1, rayonOuCote + aleaLongueur)\n          R = rotation(Q, pt2, aleaAngle)\n          if (!R.estDansQuadrilatere(A, B, C, D)) {\n            aleaAngle = 180 - aleaAngle\n            R = rotation(Q, pt2, aleaAngle)\n          }\n          figAire1 = polygone(pt2, pt1, R)\n          figAire1.color = 'none'\n          figAire1.couleurDeRemplissage = colorToLatexOrHTML('white')\n          figAire1.opaciteDeRemplissage = 1.1\n          choixFig2 = randint(0, 3, [choixFig])\n          choixFigAire2 = [\n            [E, M],\n            [G, N],\n            [I, O],\n            [K, P]\n          ]\n          S = pointSurSegment(choixFigAire2[choixFig2][0], choixFigAire2[choixFig2][1], rayonOuCote + aleaLongueur)\n          T = rotation(S, choixFigAire2[choixFig2][0], aleaAngle)\n          if (!T.estDansQuadrilatere(A, B, C, D) || T.estDansTriangle(pt2, pt1, R) || R.estDansTriangle(choixFigAire2[choixFig2][0], choixFigAire2[choixFig2][1], T)) {\n            // If the triangles intersect, we create the symmetry of the first with respect to the center of the rectangle.\n            S = milieu(A, C)\n            choixFigAire2[choixFig2][1] = homothetie(pt1, S, -1)\n            choixFigAire2[choixFig2][0] = homothetie(pt2, S, -1)\n            T = homothetie(R, S, -1)\n          }\n          figAire2 = polygone(choixFigAire2[choixFig2][0], choixFigAire2[choixFig2][1], T)\n          figAire2.color = 'none'\n          figAire2.couleurDeRemplissage = colorToLatexOrHTML('white')\n          figAire2.opaciteDeRemplissage = 1.1\n          objets.push(figAire1, figAire2, segment(pt2, R), segment(pt1, R), codageSegment(pt2, R, '|||'), codageSegment(pt2, pt1, 'OO'), codageSegment(pt1, R, 'XX'), rect)\n          objets.push(segment(choixFigAire2[choixFig2][0], T), segment(choixFigAire2[choixFig2][1], T), codageSegment(choixFigAire2[choixFig2][1], T, 'XX'), codageSegment(choixFigAire2[choixFig2][1], choixFigAire2[choixFig2][0], 'OO'), codageSegment(choixFigAire2[choixFig2][0], T, '|||'))\n          texte = mathalea2d(paramsEnonce, objets)\n          // Correction\n          texteCorr = (this.sup2 === 3) ? numAlpha(0) : ''\n          texteCorr += (this.sup2 === 1 || this.sup2 === 3 || aireOuPerimetre !== 'Area') ? 'You have to cover more ground to go around the colored figure than around the hatched rectangle. Therefore, the colored figure has a larger perimeter than that of the hatched rectangle.' : ''\n          texteCorr += (this.sup2 === 3) ? '<br>' + numAlpha(1) : ''\n          texteCorr += (this.sup2 === 2 || this.sup2 === 3 || aireOuPerimetre !== 'Perimeter') ? 'The hatched rectangle covers more area than the colored figure. Therefore, the hatched rectangle has an area greater than that of the colored figure.' : ''\n          // Interactive MCQ\n          if (this.interactif) {\n            reponsePerimetre2 = true\n            reponseAire1 = true\n          }\n          break\n      }\n      // Management of interactive multiple choice questions\n      if (this.interactif) {\n        if (this.sup2 === 1 || this.sup2 === 3 || aireOuPerimetre !== 'Area') {\n          this.autoCorrection[compteurInteractif] = {\n            enonce: 'Never mind',\n            propositions: [\n              {\n                texte: 'The hatched rectangle',\n                statut: reponsePerimetre1, // true ou false pour indiquer si c'est une bonne réponse (true)\n                feedback: ''\n              },\n              {\n                texte: 'The colored figure',\n                statut: reponsePerimetre2, // true ou false pour indiquer si c'est une bonne réponse (true)\n                feedback: ''\n              },\n              {\n                texte: 'As much as one as the other',\n                statut: reponsePerimetre3, // true ou false pour indiquer si c'est une bonne réponse (true)\n                feedback: ''\n              }\n            ]\n          }\n          monQcmPerimetre = propositionsQcm(this, compteurInteractif)\n          compteurInteractif++\n        }\n        if (this.sup2 === 2 || this.sup2 === 3 || aireOuPerimetre !== 'Perimeter') {\n          this.autoCorrection[compteurInteractif] = {\n            enonce: 'Never mind',\n            propositions: [\n              {\n                texte: 'The hatched rectangle',\n                statut: reponseAire1, // true ou false pour indiquer si c'est une bonne réponse (true)\n                feedback: ''\n              },\n              {\n                texte: 'The colored figure',\n                statut: reponseAire2, // true ou false pour indiquer si c'est une bonne réponse (true)\n                feedback: ''\n              },\n              {\n                texte: 'As much as one as the other',\n                statut: reponseAire3, // true ou false pour indiquer si c'est une bonne réponse (true)\n                feedback: ''\n              }\n            ]\n          }\n          monQcmAire = propositionsQcm(this, compteurInteractif)\n          compteurInteractif++\n        }\n      }\n      // Management of statements\n      texte += '<br>'\n      if (this.sup2 === 3) texte += numAlpha(0)\n      if (this.sup2 === 1 || this.sup2 === 3 || aireOuPerimetre !== 'Area') {\n        texte += 'Between the hatched rectangle and the colored figure, which has the largest perimeter?'\n        if (this.interactif) {\n          texte += monQcmPerimetre.texte\n        }\n      }\n      if (this.sup2 === 3) texte += '<br>' + numAlpha(1)\n      if (this.sup2 === 2 || this.sup2 === 3 || aireOuPerimetre !== 'Perimeter') {\n        texte += 'Between the hatched rectangle and the colored figure, which has the largest area?'\n        if (this.interactif) {\n          texte += monQcmAire.texte\n        }\n      }\n      if (this.questionJamaisPosee(q, texte)) {\n        this.listeQuestions.push(texte)\n        this.listeCorrections.push(texteCorr)\n        q++\n      }\n      cpt++\n    }\n    listeQuestionsToContenu(this) // On envoie l'exercice à la fonction de mise en page\n  }\n\n  this.besoinFormulaireTexte = ['Type of figures',\n  `Nombres séparés par des tirets :\n  1 : Polygone inscrit dans un rectangle\n  2 : Rectangle inscrit dans un polygone\n  3 : Rectangle avec deux demi-disques alternés qui s'emboitent\n  4 : Rectangle avec deux demi-disques alternés qui ne s'emboitent pas\n  5 : Rectangle avec deux demi-disques en plus\n  6 : Rectangle avec deux demi-disques en moins\n  7 : Quadrilatère inscrit dans un rectangle\n  8 : Rectangle inscrit dans un quadrilatère\n  9 : Rectangle avec deux triangles alternés qui s'emboîtent\n  10 : Rectangle avec deux triangles alternés qui ne s'emboîtent pas\n  11 : Rectangle avec deux triangles en plus\n  12 : Rectangle avec deux triangles en moins\n  13 : Mélange `]\n  this.besoinFormulaire2Numerique = ['Perimeters and/or areas', 4, '1: Only perimeters\\n2: Only areas\\n3: Both\\n4: One or the other at random 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