File: /home/mmtprep/public_html/mathzen.mmtprep.com/assets/3L13-3-m_vuD3ji.js.map
{"version":3,"file":"3L13-3-m_vuD3ji.js","sources":["../../src/exercices/3e/3L13-3.js"],"sourcesContent":["import { codageSegments } from '../../lib/2d/codages.js'\nimport { point } from '../../lib/2d/points.js'\nimport { polygone, polygoneAvecNom } from '../../lib/2d/polygones.js'\nimport { segment } from '../../lib/2d/segmentsVecteurs.js'\nimport { texteParPosition } from '../../lib/2d/textes.js'\nimport { homothetie } from '../../lib/2d/transformations.js'\nimport { choice } from '../../lib/outils/arrayOutils'\nimport { ecritureAlgebrique } from '../../lib/outils/ecritures'\nimport { arrondi, nombreDeChiffresDe } from '../../lib/outils/nombres'\nimport { sp } from '../../lib/outils/outilString.js'\nimport { prenom } from '../../lib/outils/Personne'\nimport { texPrix } from '../../lib/format/style'\nimport { stringNombre, texNombre } from '../../lib/outils/texNombre'\nimport { ajouteChampTexteMathLive } from '../../lib/interactif/questionMathLive.js'\nimport { gestionnaireFormulaireTexte, listeQuestionsToContenu } from '../../modules/outils.js'\nimport { aleaVariables, resoudre } from '../../modules/outilsMathjs.js'\nimport Exercice from '../Exercice'\nimport { mathalea2d } from '../../modules/2dGeneralites.js'\nimport Grandeur from '../../modules/Grandeur'\nimport { context } from '../../modules/context.js'\nimport { setReponse } from '../../lib/interactif/gestionInteractif.js'\n\nexport const titre = 'Equate a problem and solve it'\nexport const interactifReady = true\nexport const interactifType = 'mathLive'\nexport const amcReady = true\nexport const amcType = 'AMCHybride'\n\nexport const dateDePublication = '15/02/2022'\nexport const dateDeModifImportante = '06/04/2023'\n/**\n * @author Jean-Claude Lhote\n * Différents problèmes à résoudre.\n * Mise en équation de degré 1 à une inconnue, résolution et vérification.\n * Réf : 3L13-3\n * Ajout du choix des types de problèmes par Guillaume Valmont le 06/04/2023\n * Ajout d'un paramètre permettant d'avoir uniquement des nombres entiers dans l'énoncé par Guillaume-Valmont le 06/04/2023\n * Date de publication 15/02/2022\n */\nexport const uuid = '22412'\nexport const ref = '3L13-3'\nexport default class ProblemesEnEquation extends Exercice {\n constructor () {\n super()\n this.nbQuestions = 2\n this.besoinFormulaireTexte = ['Choice of problems', 'Numbers separated by hyphens\\n1: basket\\n2: basket2\\n3: purchases\\n4: polygon\\n5: programs (product vs product,\\n ... positive integer solution)\\n6: programs (product vs product,\\n ... negative integer solution)\\n7: programs (sum vs product,\\n ... positive integer solution)\\n8: programs (sum vs product,\\n ... negative integer solution)\\n9: prices\\n10: show\\n11: isosceles\\n12: Thales\\n13: Thales2\\n14: Combination']\n this.sup = '14'\n this.besoinFormulaire2CaseACocher = ['Only integers']\n this.sup2 = false\n }\n\n figureThales (a, b, c, OC) {\n const O = point(1.5, 0, 'O')\n const B = point(4, 6, 'B')\n const A = point(0, 5, 'A')\n const D = homothetie(B, O, 0.4, 'D')\n const C = homothetie(A, O, 0.4, 'C')\n const OAB = polygoneAvecNom(O, C, A, B, D)\n const CD = segment(C, D)\n const longOC = texteParPosition(`${OC}`, 0.5, 1)\n const longCA = texteParPosition(`${b}`, 0, 3)\n const longAB = texteParPosition(`${c}`, 2, 6)\n const longCD = texteParPosition(`${a}`, 1.5, 2.5)\n return mathalea2d({\n xmin: -1,\n xmax: 5,\n ymin: -1,\n ymax: 7,\n pixelsParCm: 20,\n scale: 0.8,\n zoom: 1\n }, OAB[0], OAB[1], longOC, longCA, longAB, longCD, CD)\n }\n\n triangleIsocele1 () {\n const O = point(6, 1.5)\n const B = point(0, 0)\n const A = point(0, 3)\n const OAB = polygone(O, A, B)\n const codage = codageSegments('//', 'black', O, A, O, B)\n return mathalea2d({ xmin: -1, xmax: 7, ymin: -1, ymax: 4, pixelsParCm: 20, scale: 0.8, zoom: 1 }, OAB, codage)\n }\n\n triangleIsocele2 () {\n const O = point(3, 1.5)\n const B = point(6, 0)\n const A = point(0, 0)\n const OAB = polygone(O, A, B)\n const codage = codageSegments('//', 'black', O, A, O, B)\n return mathalea2d({ xmin: -1, xmax: 7, ymin: -1, ymax: 2.5, pixelsParCm: 20, scale: 0.8, zoom: 1 }, OAB, codage)\n }\n\n nouvelleVersion () {\n this.listeQuestions = []\n this.listeCorrections = []\n this.autoCorrection = []\n const listeDeProblemes = gestionnaireFormulaireTexte({\n saisie: this.sup,\n min: 1,\n max: 12,\n melange: 14,\n defaut: 1,\n shuffle: true,\n nbQuestions: this.nbQuestions\n })\n for (let i = 0, cpt = 0, uniteOptions, texte, x, a, b, c, d, variables, enonce, figure, intro, conclusion, equation, resolution, verification, texteCorr; i < this.nbQuestions && cpt < 50;) {\n const quidam = prenom(2)\n // const n = 0 // an integer parameter which can be used in certain cases.\n const produit = choice(['strawberries', 'peaches', 'pears', 'apples', 'mangoes', 'plums', 'lemons'])\n const polygones = ['triangle', 'quadrilateral', 'Pentagon', 'hexagon']\n const clubs = ['film club', 'fitness club', 'ski club']\n uniteOptions = ['', '', '']\n switch (listeDeProblemes[i]) {\n case 1: // basket\n variables = aleaVariables(\n {\n x: 'randomInt(5,15)',\n a: 'randomInt(5,12)',\n b: 'randomInt(15,30)',\n d: 'b+(a+x)*2+x*3'\n }\n , { valueOf: true, type: 'number' })\n x = variables.x // nombre de paniers à trois points\n a = variables.a // nombres de paniers à deux points de plus que x\n b = variables.b // nombre de points marqués au lancer franc\n c = 0 // ne sert pas dans ce cas\n d = variables.d // nombre de points de la partie\n equation = `x*3+(${a}+x)*2+${b} = ${d}`\n resolution = resoudre(equation, { reduceSteps: false, substeps: true, comment: true })\n enonce = `A basketball team scored ${d} points during a match. During this match, she scored ${b} points on free throws.<br>`\n enonce += `The ${a} team scored more two-point baskets than three-point baskets.<br>How many three-point baskets did it score?`\n intro = `Let $x$ be the number of three-point baskets.<br>The number of two-point baskets is therefore $${a}+x$.<br>`\n intro += 'The team score therefore provides the equation: <br>'\n conclusion = `<br>The team therefore scored ${x} three-point baskets.`\n figure = ''\n verification = `<br>Verification:<br>$${resolution.verifLeftSide.printExpression} = ${resolution.verifLeftSide.printResult}$`\n // unitOptions[2] = 'three-point baskets'\n break\n case 2: // basket2\n variables = aleaVariables(\n {\n x: 'randomInt(17,27)',\n a: 'randomInt(5,12)',\n b: 'randomInt(15,30)',\n d: 'b+(x-a)*3+x*2'\n }\n , { valueOf: true })\n x = variables.x // nombre de paniers à deux points\n a = variables.a // nombres de paniers à trois points de moins que de paniers à 2 points\n b = variables.b // nombre de points marqués au lancer franc\n d = variables.d // nombre de points de la partie\n c = 0 // ne sert pas dans ce cas\n equation = `x*2+(x-${a})*3+${b} = ${d}`\n resolution = resoudre(equation, { reduceSteps: false, substeps: true, comment: true, suppr1: false })\n enonce = `A basketball team scored ${d} points during a match. During this match, she scored ${b} points on free throws.<br>`\n enonce += `The ${a} team scored fewer three-point baskets than two-point baskets.<br>How many two-point baskets did it score?`\n intro = `Let $x$ be the number of two-point baskets.<br>The number of three-point baskets is therefore $x-${a}$.<br>`\n intro += 'The team score therefore provides the equation: <br>'\n conclusion = `<br>The team therefore scored ${x} two-point baskets.`\n figure = ''\n verification = `<br>Verification:<br>$${resolution.verifLeftSide.printExpression} = ${resolution.verifLeftSide.printResult}$`\n // unitOptions[2] = 'two-point baskets'\n break\n\n case 3: // achats\n variables = aleaVariables(\n {\n a: `randomInt(2,5)${this.sup2 ? '' : '+randomInt(0,4)/5'}`,\n x: `randomInt(2,5)${this.sup2 ? '' : '+randomInt(0,1)/2'}`,\n b: 'a*x',\n test: 'b<100 and b>5 and b%10!=0'\n }\n , { valueOf: true })\n x = variables.x // prix de 1kg de produit\n a = variables.a // nombre de kg de produit\n b = variables.b // prix total du produit\n d = b > 50 ? 100 : b > 20 ? 50 : b > 10 ? 20 : 10 // valeur du billet donné\n c = 0 // ne sert pas dans ce cas\n equation = `${a}*x+${arrondi(d - b, 2)} = ${d}`\n resolution = resoudre(equation, { substeps: true, comment: true })\n enonce = `${quidam[0]} bought $${texNombre(a)}$ kg of ${produit} with a $${d}$ € note. The merchant gave him back $${texPrix(d - b)}$ €.<br>`\n enonce += `What is the price of a kilogram of ${produit}?`\n intro = `Let $x$ be the price of a kilogram of ${produit}.<br>The statement translates into the following equation:<br>`\n conclusion = `<br>The price of a kilogram of ${produit} is therefore $${texNombre(x)}$ €.`\n figure = ''\n verification = `<br>Verification:<br>$${resolution.verifLeftSide.printExpression} = ${resolution.verifLeftSide.printResult}$`\n uniteOptions[2] = '€'\n break\n case 4: // polygone\n variables = aleaVariables(\n {\n x: `randomInt(2,4)${this.sup2 ? '' : '+randomInt(0.45)/5'}`,\n a: `randomInt(2,5)${this.sup2 ? '' : '+randomInt(0.45)/5'}`,\n b: 'randomInt(2,5)',\n d: 'b*x+a'\n }\n , { valueOf: true })\n x = variables.x // longueur d'un des côtés égaux\n a = variables.a // longueur du côté différent\n b = variables.b // nombre de côtés égaux du polygone\n d = variables.d // périmètre du polygone\n c = 0 // ne sert pas dans ce cas\n equation = `${b}*x+${a} = ${stringNombre(d).replace(',', '.').replace(/\\s+/g, '')}`\n resolution = resoudre(equation, { reduceSteps: true, substeps: false, comment: true })\n enonce = `A ${polygones[b - 2]} has one side of length $${texNombre(a)}$ cm and all its other sides have the same length.<br>Its perimeter is $${texNombre(d)}$ cm.<br>`\n enonce += 'What is the length' + (context.isAmc ? ', in cm,' : '') + ' sides of the same length?'\n intro = 'Let $x$ be the length of the sides of the same length.<br>'\n intro += `A ${polygones[b - 2]} has ${b + 1} sides, so this one has ${b} sides of the same length.<br>`\n intro += 'The statement translates into the following equation:<br>'\n conclusion = `<br>The sides of the same length therefore measure $${texNombre(x)}$ cm.`\n figure = ''\n verification = `<br>Verification:<br>$${resolution.verifLeftSide.printExpression} = ${resolution.verifLeftSide.printResult}$`\n uniteOptions = [' units[Lengths]', new Grandeur(x, 'cm'), '']\n break\n case 5: // programmes\n variables = aleaVariables(\n {\n a: 'randomInt(2,15)',\n b: 'randomInt(1,10)',\n c: 'randomInt(2,15)',\n d: 'randomInt(1,10)',\n test: 'abs((c*d-a*b))%abs(a-c) == 0 and (c*d-a*b)*(a-c)>0'\n }\n , { valueOf: true })\n // falls through\n case 6: // programmes2\n if (listeDeProblemes[i] === 6) {\n variables = aleaVariables(\n {\n a: 'randomInt(2,15)',\n b: 'randomInt(1,10)',\n c: 'randomInt(2,15)',\n d: 'randomInt(1,10)',\n test: 'abs((c*d-a*b))%abs(a-c) == 0 and (c*d-a*b)*(a-c)<0'\n }\n , { valueOf: true })\n }\n a = variables.a\n b = variables.b\n c = variables.c\n d = variables.d\n x = Math.round((c * d - a * b) / (a - c))\n equation = `(x+${b})*${a}=(x+${d})*${c}`\n resolution = resoudre(equation, { reduceSteps: false, substeps: false, comment: true })\n enonce = `${quidam[0]} and ${quidam[1]} choose the same number.<br> ${quidam[0]} adds ${b} to it then multiplies the result by ${a} while `\n enonce += `${quidam[1]} adds ${d} to it then multiplies the result by ${c}.<br>`\n enonce += `${quidam[0]} and ${quidam[1]} achieve the same result.<br>`\n enonce += `What common number did ${quidam[0]} and ${quidam[1]} choose?`\n intro = 'Let $x$ be the number chosen at the start.<br>'\n intro += `The calculation program carried out by ${quidam[0]} translates into: $(x+${b})\\\\times ${a}$.<br>`\n intro += `The calculation program carried out by ${quidam[1]} translates into: $(x+${d})\\\\times ${c}$.<br>`\n intro += 'The equality of results results in the following equation:<br>'\n conclusion = `<br>${quidam[0]} and ${quidam[1]} we therefore initially chose the ${x} number.`\n figure = ''\n verification = `<br>Verification:<br>On the one hand: $${resolution.verifLeftSide.printExpression} = ${resolution.verifLeftSide.printResult}$<br>On the other hand: $${resolution.verifRightSide.printExpression} = ${resolution.verifRightSide.printResult}$`\n break\n case 7: // programmes\n variables = aleaVariables(\n {\n a: 'randomInt(2,15)',\n b: 'randomInt(1,10)',\n c: 'randomInt(2,15)',\n d: 'randomInt(1,10)',\n test: 'abs((d-a*b))%abs(a-c) == 0 and (d-a*b)*(a-c)>0'\n }\n , { valueOf: true })\n // falls through\n case 8: // programmes\n if (listeDeProblemes[i] === 8) {\n variables = aleaVariables(\n {\n a: 'randomInt(2,15)',\n b: 'randomInt(1,10)',\n c: 'randomInt(2,15)',\n d: 'randomInt(1,10)',\n test: 'abs((d-a*b))%abs(a-c) == 0 and (d-a*b)*(a-c)<0'\n }\n , { valueOf: true })\n }\n a = variables.a\n b = variables.b\n c = variables.c\n d = variables.d\n x = Math.round((d - a * b) / (a - c))\n equation = `(x+${b})*${a} = ${c}*x+${d}`\n resolution = resoudre(equation, { reduceSteps: false, substeps: false, comment: true })\n enonce = `${quidam[0]} and ${quidam[1]} choose the same number.<br> ${quidam[0]} adds ${b} to it then multiplies the result by ${a} while `\n enonce += `${quidam[1]} multiplies it by ${c} then adds to the result ${d}.<br>`\n enonce += `${quidam[0]} and ${quidam[1]} achieve the same result.<br>`\n enonce += `What common number did ${quidam[0]} and ${quidam[1]} choose?`\n intro = 'Let $x$ be the number chosen at the start.<br>'\n intro += `The calculation program carried out by ${quidam[0]} translates into: $(x+${b})\\\\times ${a}$.<br>`\n intro += `The calculation program carried out by ${quidam[1]} translates into: $${c}x + ${d}$.<br>`\n intro += 'The equality of results results in the following equation:<br>'\n conclusion = `<br>${quidam[0]} and ${quidam[1]} we therefore initially chose the ${x} number.`\n figure = ''\n verification = `<br>Verification:<br>On the one hand: $${resolution.verifLeftSide.printExpression} = ${resolution.verifLeftSide.printResult}$<br>On the other hand: $${resolution.verifRightSide.printExpression} = ${resolution.verifRightSide.printResult}$`\n break\n case 9: // tarifs\n variables = aleaVariables(\n {\n a: 'randomInt(0,2)',\n b: this.sup2 ? 'randomInt(5,8)' : 'randomInt(50,80)/10',\n c: 'randomInt(4,10)*5',\n d: `b-${this.sup2 ? 'randomInt(1,3)' : 'randomInt(2,6)*0.5'}`,\n test: 'c/(b-d)<30 and c/(b-d)>10 and (c*2)%((b-d)*2)==0'\n }\n , { valueOf: true })\n a = variables.a\n b = variables.b\n c = variables.c\n d = variables.d\n x = Math.ceil(c / (b - d))\n equation = `x*${b}>=${c}+x*${stringNombre(d).replace(',', '.').replace(/\\s+/g, '')}`\n resolution = resoudre(equation, { reduceSteps: false, substeps: false, comment: true })\n enonce = `The ${clubs[a]} of a village offers two prices to its practitioners.<br>`\n enonce += `Rate A offers to pay $${texPrix(b)}$ € at each session.<br>`\n enonce += `Rate B offers to pay an annual subscription of $${texPrix(c)}$ € then to pay $${texPrix(d)}$ € per session.<br>`\n enonce += 'For what number of sessions does rate B become more advantageous than rate A?'\n intro = 'Let $x$ be the number of sessions.<br>'\n intro += `The price to pay with rate A is: $x\\\\times ${texPrix(b)}$.<br>`\n intro += `The price to pay with rate B is: $${texPrix(c)}+x\\\\times ${texPrix(d)}$.<br>`\n intro += 'For fare B to be more advantageous, $x$ must satisfy the following inequality:<br>'\n conclusion = `<br>It is from $${x}$ sessions that rate B becomes more advantageous than rate A (for $${x}$ sessions, the two rates are equivalent).`\n figure = ''\n verification = `<br>Verification:<br>On the one hand: $${resolution.verifLeftSide.printExpression} = ${resolution.verifLeftSide.printResult}$<br>On the other hand: $${resolution.verifRightSide.printExpression} = ${resolution.verifRightSide.printResult}$`\n // verification = `<br>Verification:<br>$${x}\\\\times ${texPrix(b)} = ${texPrix(x * b)}$ and $${c}+${x}\\\\times ${texPrix(d)} = ${c}+${texPrix(x * d)}= ${texPrix(c + x * d)}$.<br>`\n break\n case 10: // spectacle\n variables = aleaVariables(\n {\n a: 'randomInt(200,300)*10',\n b: this.sup2 ? 'randomInt(10,20)' : 'randomInt(100,200)/10',\n c: this.sup2 ? 'randomInt(5,15)' : 'randomInt(50,150)/10',\n x: 'randomInt(1000,a-500)',\n d: 'b*x+(a-x)*c',\n test: 'b>c'\n }\n , { valueOf: true })\n a = variables.a\n b = variables.b\n c = variables.c\n d = variables.d\n x = variables.x\n equation = `x*${b}+(${a}-x)*${c} = ${stringNombre(d).replace(',', '.').replace(/\\s+/g, '')}`\n resolution = resoudre(equation, { reduceSteps: false, substeps: true, comment: true })\n enonce = `In a performance hall with $${texNombre(a)}$ seats, the entry price for an adult is $${texPrix(b)}$ € and for a child it is $${texPrix(c)}$ €.<br>`\n enonce += `Tonight's show took place in front of a full house and the revenue is $${texPrix(d)}$ €.<br>`\n enonce += 'How many adults were there in the room?'\n intro = 'Let $x$ be the number of adult places sold.<br>'\n intro += `As the $${texNombre(a)}$ places have been sold, the number of children's places is: $${a}-x$.<br>`\n intro += 'Calculating the recipe gives the following equation.<br>'\n conclusion = `<br>So there were $${texNombre(x)}$ adults at the show.`\n figure = ''\n verification = `<br>Verification:<br>$${resolution.verifLeftSide.printExpression} = ${resolution.verifLeftSide.printResult}$`\n break\n case 11: // isocele\n variables = aleaVariables(\n {\n a: 'randomInt(50,100)',\n c: '(1-2*round(randomInt(0,2)))*randomInt(10,30)',\n b: 'a+c',\n d: 'd=2*a+b',\n test: 'a+a>b and b>0'\n }\n , { valueOf: true })\n a = variables.a\n b = variables.b\n c = variables.c\n d = variables.d\n enonce = `An isosceles triangle has perimeter $${d}$ mm.`\n if (c > 0) { // La base est le plus grand côté\n enonce += `Its base is greater than the equal sides of $${c}$ mm.`\n } else { // La base est plus petite que les autres côtés\n enonce += `Its base is smaller than the equal sides of $${-c}$ mm.`\n }\n if (choice([true, false])) {\n enonce += '<br>What is the measurement of its base' + (context.isAmc ? ', in mm' : '') + ' ? (The figure is not full size.)'\n intro = `Let $x$ be the length of its base. The length of equal sides is: $x${ecritureAlgebrique(-c)}$.<br>`\n intro += 'Calculating the perimeter gives the following equation:<br>'\n equation = `2*(x${ecritureAlgebrique(-c)})+x=${d}`\n conclusion = `<br>The base of this isosceles triangle therefore measures $${b}$ mm.`\n x = b\n } else {\n enonce += '<br>What is the measure of its equal sides? (the figure is not in real size)'\n intro = `Let $x$ be the length of one of the equal sides. The length of the base is: $x${ecritureAlgebrique(c)}$.<br>`\n intro += 'Calculating the perimeter gives the following equation:<br>'\n equation = `2*x+x${ecritureAlgebrique(c)} = ${d}`\n conclusion = `<br>The two equal sides of this isosceles triangle therefore measure $${a}$ mm.`\n x = a\n }\n resolution = resoudre(equation, { reduceSteps: false, substeps: true, comment: true, suppr1: false })\n if (c > 0) figure = this.triangleIsocele2()\n else figure = this.triangleIsocele1()\n verification = `<br>Verification:<br>$${resolution.verifLeftSide.printExpression} = ${resolution.verifLeftSide.printResult}$`\n uniteOptions = [' units[Lengths]', new Grandeur(x, 'mm'), '']\n break\n case 12: // Thalès\n variables = variables = aleaVariables(\n {\n a: 'randomInt(5,40)',\n b: 'randomInt(5,40)',\n c: 'randomInt(41,100)',\n d: 'a*b/(c-a)',\n test: 'd>0 and (a*b)%abs(c-a)==0'\n }\n , { valueOf: true })\n a = variables.a\n b = variables.b\n c = variables.c\n d = variables.d\n x = Math.round(d)\n equation = `(x+${b})*${a}=x*${c}`\n resolution = resoudre(equation, { reduceSteps: false, substeps: false, comment: true })\n figure = this.figureThales(a, b, c, '')\n enonce = 'Consider the figure below which is not in full size where $[CD]$ and $[AB]$ are parallel.'\n enonce += ` $AB=${c}\\\\text{mm}$, $AC=${b}\\\\text{mm}$ and $CD=${a}\\\\text{mm}$.<br> Determine the length $OC$${context.isAmc ? ', in mm.' : '.'}`\n intro = 'In this Thales configuration, we have the following equality: $\\\\dfrac{OC}{OA}=\\\\dfrac{CD}{AB}$.<br>'\n intro += 'This equality is equivalent to the equality of cross products: $OC\\\\times AB = CD\\\\times OA$.<br>'\n intro += 'By replacing the lengths with the data in the statement and setting $x=OC$, we obtain the following equation:<br>'\n conclusion = `<br>so $OA=${x}\\\\text{mm}$.<br>`\n verification = `<br>Verification:<br>On the one hand: $${resolution.verifLeftSide.printExpression} = ${resolution.verifLeftSide.printResult}$<br>On the other hand: $${resolution.verifRightSide.printExpression} = ${resolution.verifRightSide.printResult}$`\n uniteOptions = [' units[Lengths]', new Grandeur(x, 'mm'), '']\n break\n case 13: // Thales2\n variables = variables = aleaVariables(\n {\n a: 'randomInt(5,40)',\n b: 'randomInt(5,40)',\n c: 'randomInt(41,100)',\n d: 'a*b/(c-a)',\n test: 'd>0 and (a*b)%abs(c-a)==0'\n }\n , { valueOf: true })\n a = variables.a\n x = variables.b\n c = variables.c\n d = variables.d\n b = Math.round(d)\n equation = `(x+${b})*${a} = ${b}*${c}`\n resolution = resoudre(equation, { reduceSteps: false, substeps: false, comment: true })\n figure = this.figureThales(a, '', c, b)\n enonce = 'Consider the figure below which is not in full size where $[CD]$ and $[AB]$ are parallel.'\n enonce += ` $AB=${c}\\\\text{mm}$, $OC=${b}\\\\text{mm}$ and $CD=${a}\\\\text{mm}$.<br> Determine the length $AC$${context.isAmc ? ', in mm.' : '.'}`\n intro = 'In this Thales configuration, we have the following equality: $\\\\dfrac{OA}{OC}=\\\\dfrac{AB}{CD}$.<br>'\n intro += 'This equality is equivalent to the equality of cross products: $CD\\\\times OA = OC\\\\times AB$.<br>'\n intro += 'By replacing the lengths with the data in the statement and setting $x=OC$, we obtain the following equation:<br>'\n conclusion = `<br>so $CA=${x}\\\\text{mm}$.<br>`\n verification = `<br>Verification:<br>$${resolution.verifLeftSide.printExpression} = ${resolution.verifLeftSide.printResult}$`\n uniteOptions = [' units[Lengths]', new Grandeur(x, 'mm'), '']\n break\n }\n\n texte = enonce + figure + ajouteChampTexteMathLive(this, i, 'largeur10 inline' + uniteOptions[0], { texteApres: sp(2) + uniteOptions[2] })\n texteCorr = intro\n texteCorr += `$${resolution.equation}$`\n texteCorr += '<br>Let\\'s solve the equation:<br>'\n texteCorr += resolution.texteCorr\n texteCorr += verification\n texteCorr += conclusion\n\n if (context.isAmc) {\n this.autoCorrection[i] = {\n enonce: texte + 'ddddddd<br>',\n enonceAvant: false,\n propositions: [\n {\n type: 'AMCOpen',\n propositions: [{\n enonce: texte + '<br>Equate the problem below and solve it.',\n statut: 3,\n pointilles: true\n }]\n },\n {\n type: 'AMCNum',\n propositions: [{\n texte: '',\n statut: '',\n reponse: {\n texte: 'Answer to the problem:',\n valeur: [x],\n param: {\n digits: Math.max(nombreDeChiffresDe(x), 2),\n signe: true\n }\n }\n }]\n }\n ]\n }\n }\n\n if (this.questionJamaisPosee(i, x, a, b, d)) {\n this.listeQuestions.push(texte)\n this.listeCorrections.push(texteCorr)\n if (uniteOptions[0] === '') setReponse(this, i, x, { formatInteractif: 'calculation' })\n else setReponse(this, i, uniteOptions[1], { formatInteractif: 'units' })\n i++\n }\n cpt++\n }\n listeQuestionsToContenu(this)\n 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