[{"data":1,"prerenderedAt":127},["ShallowReactive",2],{"\u002Fpublic\u002Ftopics\u002Fgeometria\u002Fcircunferencia?{}":3,"topics-with-content:geometria":112},{"course":4,"topic":12,"counts":17,"universities":22,"channels":35,"sampleQuestions":70,"sameName":111},{"id":5,"slug":6,"name":7,"shortName":8,"area":9,"icon":10,"sortOrder":11},3,"geometria","Geometría","Geom.","math","i-lucide-triangle",2,{"id":13,"courseId":5,"slug":14,"name":15,"sortOrder":16},307,"circunferencia","Circunferencia",6,{"topicId":13,"courseId":5,"questions":18,"classes":19,"videos":20,"minutes":21},33,229,170,3460,[23,31],{"universityId":11,"questions":24,"years":25},17,[26,27,28,29,30],2026,2025,2024,2023,2022,{"universityId":32,"questions":33,"years":34},1,16,[26,27,28,29,30],[36,39,42,45,48,51,54,56,58,61,64,66,68],{"name":37,"classes":38},"Academia ipluton",52,{"name":40,"classes":41},"Alberto Cruz",51,{"name":43,"classes":44},"Academia Grupo Ciencias",36,{"name":46,"classes":47},"Ciclo Uni-San Marcos",35,{"name":49,"classes":50},"Academias Aduni y César Vallejo",14,{"name":52,"classes":53},"Academia Internet",10,{"name":55,"classes":16},"META VILLARREAL",{"name":57,"classes":16},"Salón Sapiens",{"name":59,"classes":60},"Pamer Corporación Educativa",5,{"name":62,"classes":63},"Academia_Pitagoras",4,{"name":65,"classes":63},"CEPRE UNMSM",{"name":67,"classes":5},"Saco Oliveros",{"name":69,"classes":5},"Trilce Multimedia",[71,96],{"id":72,"courseId":5,"topicId":13,"pastExamId":73,"stem":74,"options":75,"correctKey":89,"explanation":91,"difficulty":63,"status":92,"source":93,"stats":94},1652,198,"Un pentágono regular $ABCDE$ está inscrito en una circunferencia de centro $O$. Con centro en el vértice $A$ y radio $\\overline{AO}$ se traza la circunferencia $C_{1}$ que interseca el arco $AE$ en el punto $P$. Del vértice $E$ se traza el segmento tangente $\\overline{EQ}$ a la circunferencia $C_{1}$ ($Q$ punto de tangencia). Y con centro en $E$ y radio $\\overline{EQ}$, se traza la circunferencia $C_{2}$ que interseca el arco $ED$ en el punto $M$. Calcule en grados sexagesimales la medida del arco $MEP$.",[76,79,82,85,88],{"key":77,"text":78},"A","12",{"key":80,"text":81},"B","24",{"key":83,"text":84},"C","30",{"key":86,"text":87},"D","36",{"key":89,"text":90},"E","48","","published","UNI 2026-1 · Matemática",{"attempts":95,"accuracy":95},0,{"id":97,"courseId":5,"topicId":13,"pastExamId":73,"stem":98,"options":99,"correctKey":86,"explanation":91,"difficulty":63,"status":92,"source":93,"stats":110},1656,"Determine el valor de verdad (V) o falsedad (F) de cada una de las siguientes proposiciones:\nI. Si dos circunferencias no congruentes son tangentes exteriores, entonces los segmentos tangentes no comunes trazados desde un punto exterior a ambas son congruentes.\nII. Si dos circunferencias no congruentes son tangentes, entonces toda recta que contiene al punto de tangencia, secante a ambas circunferencias, determina sobre cada una de ellas, arcos que tomados dos a dos son de igual medida en grados sexagesimales.\nIII. Desde un punto exterior a una circunferencia, se trazan las rectas tangentes. Si se traza la recta bisectriz del ángulo determinado por dichas rectas, entonces el cuadrilátero determinado por los puntos de tangencia y los puntos de intersección de la bisectriz con la circunferencia es un trapezoide simétrico.\nIndique la secuencia correcta.",[100,102,104,106,108],{"key":77,"text":101},"VFV",{"key":80,"text":103},"VVV",{"key":83,"text":105},"VVF",{"key":86,"text":107},"FVV",{"key":89,"text":109},"FFV",{"attempts":95,"accuracy":95},[],[113,114,115,116,117,118,13,119,120,121,122,123,124,125,126],301,302,303,304,305,306,308,309,310,311,312,313,314,315,1791501527149]