246:@0.052592:0.966074:0.080768:0.966074:0.080768:0.949450:0.052592:0.949450:0.000000:0.000000:0.000000
Olimpiadas matemáticas:@0.107368:0.074738:0.438969:0.074738:0.438969:0.046697:0.107368:0.046697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1. :@0.096359:0.125354:0.115100:0.125354:0.115100:0.108218:0.096359:0.108218:0.000000:0.000000:0.000000
El cuadrado ABCD tiene lados de longitud 6 cm. :@0.124848:0.125354:0.489789:0.125354:0.489789:0.109684:0.124848:0.109684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los puntos M y N están sobre AD y AB, respectiva-:@0.124848:0.141951:0.485752:0.141951:0.485752:0.126281:0.124848:0.126281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mente, de forma que CN y CM dividen al cuadra-:@0.124848:0.158547:0.485715:0.158547:0.485715:0.142877:0.124848:0.142877:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
do en tres regiones de la misma área. ¿Cuál es la :@0.124848:0.175143:0.489752:0.175143:0.489752:0.159474:0.124848:0.159474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
longitud de NB?:@0.124848:0.191740:0.242785:0.191740:0.242785:0.176070:0.124848:0.176070:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2. :@0.096359:0.291304:0.115100:0.291304:0.115100:0.274168:0.096359:0.274168:0.000000:0.000000:0.000000
El diagrama muestra un rectángulo de dimen-:@0.124848:0.291304:0.485733:0.291304:0.485733:0.275634:0.124848:0.275634:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
siones 9 × 15, que contiene dos circunferencias. :@0.124848:0.307900:0.489771:0.307900:0.489771:0.292231:0.124848:0.292231:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cada una de las circunferencias toca al rectángulo :@0.124848:0.324497:0.489752:0.324497:0.489752:0.308827:0.124848:0.308827:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en tres de sus lados. ¿Cuál es la distancia entre los :@0.124848:0.341093:0.489715:0.341093:0.489715:0.325423:0.124848:0.325423:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
centros de las circunferencias?:@0.124848:0.357690:0.346752:0.357690:0.346752:0.342020:0.124848:0.342020:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3. :@0.096359:0.457254:0.115100:0.457254:0.115100:0.440118:0.096359:0.440118:0.000000:0.000000:0.000000
Dentro de un cuadrado de lado 6 cm se trazaron :@0.124848:0.457254:0.489787:0.457254:0.489787:0.441584:0.124848:0.441584:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
semicírculos (con 3 de los lados como diámetros) :@0.124848:0.473850:0.489808:0.473850:0.489808:0.458181:0.124848:0.458181:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y se sombreó como muestra la figura. ¿Cuál es el :@0.124848:0.490447:0.489734:0.490447:0.489734:0.474777:0.124848:0.474777:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
área de la figura sombreada?:@0.124848:0.507043:0.335548:0.507043:0.335548:0.491373:0.124848:0.491373:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4. :@0.096359:0.608226:0.115100:0.608226:0.115100:0.591090:0.096359:0.591090:0.000000:0.000000:0.000000
Luisa dibuja flores: una azul, una verde, una roja, una amarilla, una azul, una verde, etc. ¿De qué color es la :@0.124848:0.608226:0.907112:0.608226:0.907112:0.592556:0.124848:0.592556:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
29.  flor?:@0.124848:0.624822:0.186135:0.624816:0.186135:0.609146:0.124848:0.609152:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.146043:0.618768:0.150921:0.618768:0.150921:0.609633:0.146043:0.609633:0.000000
5. :@0.096356:0.692806:0.115097:0.692806:0.115097:0.675670:0.096356:0.675670:0.000000:0.000000:0.000000
En la figura, PQRS es un paralelogramo. ¿Cuánto :@0.124845:0.692806:0.489767:0.692806:0.489767:0.677136:0.124845:0.677136:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vale el ángulo x?:@0.124845:0.709402:0.246025:0.709402:0.246025:0.693732:0.124845:0.693732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
6. :@0.096356:0.834732:0.115097:0.834732:0.115097:0.817596:0.096356:0.817596:0.000000:0.000000:0.000000
En la figura ABCD es un rectángulo de área 32, M :@0.124845:0.834732:0.489806:0.834732:0.489806:0.819062:0.124845:0.819062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es punto medio de BC, DR = BM y 2AD = AB. ¿Cuál :@0.124845:0.851329:0.489694:0.851329:0.489694:0.835659:0.124845:0.835659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es el área del triángulo ARM?:@0.124845:0.867925:0.335766:0.867925:0.335766:0.852255:0.124845:0.852255:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.096356:0.243168:0.100262:0.243168:0.100262:0.226544:0.096356:0.226544:0.000000
Argumenta:@0.124845:0.243168:0.215343:0.243168:0.215343:0.226268:0.124845:0.226268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.215343:0.243168:0.219065:0.243168:0.219065:0.226033:0.215343:0.226033:0.000000
en tu cuaderno la solución.:@0.219065:0.243168:0.417676:0.243168:0.417676:0.227499:0.219065:0.227499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.096356:0.404084:0.100262:0.404084:0.100262:0.387460:0.096356:0.387460:0.000000
Argumenta:@0.124845:0.404084:0.215343:0.404084:0.215343:0.387183:0.124845:0.387183:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.215343:0.404084:0.219065:0.404084:0.219065:0.386948:0.215343:0.386948:0.000000
en tu cuaderno la solución.:@0.219065:0.404084:0.417676:0.404084:0.417676:0.388414:0.219065:0.388414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.096356:0.571292:0.100262:0.571292:0.100262:0.554668:0.096356:0.554668:0.000000
Argumenta:@0.124845:0.571292:0.215343:0.571292:0.215343:0.554392:0.124845:0.554392:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.215343:0.571292:0.219065:0.571292:0.219065:0.554157:0.215343:0.554157:0.000000
en tu cuaderno la solución.:@0.219065:0.571292:0.417676:0.571292:0.417676:0.555623:0.219065:0.555623:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
9 cm:@0.554430:0.346913:0.584162:0.346913:0.584162:0.334093:0.554430:0.334093:0.000000:0.000000:0.000000:0.000000
15 cm:@0.697150:0.405042:0.734240:0.405042:0.734240:0.392221:0.697150:0.392221:0.000000:0.000000:0.000000:0.000000:0.000000
Adaptado: http://www.ommenlinea.org/:@0.713261:0.928522:0.903641:0.928522:0.903641:0.918550:0.713261:0.918550:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C :@0.627330:0.125482:0.639225:0.125482:0.639225:0.112662:0.627330:0.112662:0.000000:0.000000
A :@0.627209:0.231092:0.639331:0.231092:0.639331:0.218271:0.627209:0.218271:0.000000:0.000000
B :@0.783604:0.231092:0.794520:0.231092:0.794520:0.218271:0.783604:0.218271:0.000000:0.000000
D :@0.782534:0.125482:0.795591:0.125482:0.795591:0.112662:0.782534:0.112662:0.000000:0.000000
M:@0.624028:0.192766:0.635758:0.192766:0.635758:0.179945:0.624028:0.179945:0.000000
N:@0.689870:0.236795:0.699489:0.236795:0.699489:0.223974:0.689870:0.223974:0.000000
P:@0.655460:0.658782:0.662637:0.658782:0.662637:0.645395:0.655460:0.645395:0.000000
83°:@0.642780:0.681900:0.661928:0.681900:0.661928:0.669079:0.642780:0.669079:0.000000:0.000000:0.000000
41°:@0.791878:0.673096:0.811026:0.673096:0.811026:0.660275:0.791878:0.660275:0.000000:0.000000:0.000000
S:@0.560263:0.726665:0.566867:0.726665:0.566867:0.713278:0.560263:0.713278:0.000000
Q:@0.825063:0.658770:0.834788:0.658770:0.834788:0.645384:0.825063:0.645384:0.000000
R:@0.760925:0.726665:0.768252:0.726665:0.768252:0.713278:0.760925:0.713278:0.000000
x:@0.714608:0.711536:0.720714:0.711536:0.720714:0.698149:0.714608:0.698149:0.000000
D:@0.599400:0.805069:0.608838:0.805069:0.608838:0.791682:0.599400:0.791682:0.000000
R:@0.659090:0.805069:0.666418:0.805069:0.666418:0.791682:0.659090:0.791682:0.000000
C:@0.801087:0.805069:0.809199:0.805069:0.809199:0.791682:0.801087:0.791682:0.000000
M:@0.799459:0.846563:0.810827:0.846563:0.810827:0.833177:0.799459:0.833177:0.000000
B:@0.801524:0.890570:0.808761:0.890570:0.808761:0.877184:0.801524:0.877184:0.000000
A:@0.595043:0.890570:0.603139:0.890570:0.603139:0.877184:0.595043:0.877184:0.000000
La longitud del segmento NB es igual a 4 cm.:@0.128487:0.256281:0.338673:0.256281:0.338673:0.246309:0.128487:0.246309:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La distancia entre los centros de la circunferencia es de 6 cm.:@0.125133:0.419717:0.408130:0.419717:0.408130:0.409746:0.125133:0.409746:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El área sombreada es de 18 cm .:@0.123503:0.581807:0.273041:0.581807:0.273041:0.571836:0.123503:0.571836:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.267666:0.577959:0.271002:0.577959:0.271002:0.572146:0.267666:0.572146:0.000000
azul:@0.128487:0.661334:0.147249:0.661334:0.147249:0.651362:0.128487:0.651362:0.000000:0.000000:0.000000:0.000000
124º :@0.128487:0.738027:0.152175:0.738027:0.152175:0.728055:0.128487:0.728055:0.000000:0.000000:0.000000:0.000000:0.000000
14 :@0.128487:0.890532:0.142500:0.890532:0.142500:0.880561:0.128487:0.880561:0.000000:0.000000:0.000000