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
206:@0.024814:0.963884:0.056738:0.963884:0.056738:0.945447:0.024814:0.945447:0.000000:0.000000:0.000000
1. :@0.096359:0.125354:0.115100:0.125354:0.115100:0.108218:0.096359:0.108218:0.000000:0.000000:0.000000
El área del rectángulo ABCD es 10 cm . Los puntos :@0.124848:0.125354:0.489218:0.125354:0.489218:0.109684:0.124848:0.109684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.393533:0.119307:0.398776:0.119307:0.398776:0.110171:0.393533:0.110171:0.000000
M y N son los puntos medios de los lados AD y BC. :@0.124848:0.141951:0.489271:0.141951:0.489271:0.126281:0.124848:0.126281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuál es el área del cuadrilátero MBND?:@0.124848:0.158547:0.412924:0.158547:0.412924:0.142877:0.124848:0.142877:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.096359:0.250090:0.100266:0.250090:0.100266:0.233466:0.096359:0.233466:0.000000
Argumenta:@0.124848:0.250090:0.215344:0.250090:0.215344:0.233189:0.124848:0.233189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.215344:0.250090:0.219067:0.250090:0.219067:0.232954:0.215344:0.232954:0.000000
la solución::@0.219067:0.250090:0.300701:0.250090:0.300701:0.234420:0.219067:0.234420:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.096359:0.416773:0.100266:0.416773:0.100266:0.400149:0.096359:0.400149:0.000000
Argumenta:@0.124848:0.416773:0.215344:0.416773:0.215344:0.399872:0.124848:0.399872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.215344:0.416773:0.219067:0.416773:0.219067:0.399637:0.215344:0.399637:0.000000
la solución::@0.219067:0.416773:0.300701:0.416773:0.300701:0.401103:0.219067:0.401103:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.096359:0.580371:0.100266:0.580371:0.100266:0.563747:0.096359:0.563747:0.000000
Argumenta:@0.124848:0.580371:0.215344:0.580371:0.215344:0.563471:0.124848:0.563471:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.215344:0.580371:0.219067:0.580371:0.219067:0.563236:0.215344:0.563236:0.000000
la solución::@0.219067:0.580371:0.300701:0.580371:0.300701:0.564702:0.219067:0.564702:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Respuesta:@0.124848:0.274722:0.203516:0.274722:0.203516:0.258097:0.124848:0.258097:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
::@0.203516:0.274722:0.206722:0.274722:0.206722:0.259052:0.203516:0.259052:0.000000
Respuesta:@0.124848:0.441404:0.203516:0.441404:0.203516:0.424780:0.124848:0.424780:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
::@0.203516:0.441404:0.206722:0.441404:0.206722:0.425735:0.203516:0.425735:0.000000
Respuesta:@0.124848:0.605003:0.203516:0.605003:0.203516:0.588379:0.124848:0.588379:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
::@0.203516:0.605003:0.206722:0.605003:0.206722:0.589333:0.203516:0.589333:0.000000
2. :@0.096359:0.309173:0.115100:0.309173:0.115100:0.292037:0.096359:0.292037:0.000000:0.000000:0.000000
El área de cada círculo de la figura es 1 cm . El área :@0.124848:0.309173:0.489228:0.309167:0.489228:0.293497:0.124848:0.293503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.426637:0.303119:0.431880:0.303119:0.431880:0.293984:0.426637:0.293984:0.000000
común a dos círculos superpuestos es (1/8) cm . :@0.124858:0.325763:0.489229:0.325763:0.489229:0.310093:0.124858:0.310093:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.476746:0.319716:0.481988:0.319716:0.481988:0.310580:0.476746:0.310580:0.000000
¿Cuál es el área de la región cubierta por los cinco :@0.124841:0.342359:0.489172:0.342359:0.489172:0.326690:0.124841:0.326690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
círculos?:@0.124841:0.358956:0.187753:0.358956:0.187753:0.343286:0.124841:0.343286:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3. :@0.096352:0.472751:0.115093:0.472751:0.115093:0.455616:0.096352:0.455616:0.000000:0.000000:0.000000
La figura muestra el triángulo ABC con la altura :@0.124841:0.472751:0.489193:0.472751:0.489193:0.457082:0.124841:0.457082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
BH y la bisectriz AD. El ángulo obtuso entre BH :@0.124841:0.489348:0.489191:0.489348:0.489191:0.473678:0.124841:0.473678:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y AD es 4 veces el ángulo DAB. ¿Cuánto mide el :@0.124841:0.505944:0.489266:0.505944:0.489266:0.490274:0.124841:0.490274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ángulo CAB?:@0.124841:0.522541:0.218251:0.522541:0.218251:0.506871:0.124841:0.506871:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4. :@0.096352:0.639448:0.115093:0.639448:0.115093:0.622312:0.096352:0.622312:0.000000:0.000000:0.000000
En un campamento de verano, 96 niños se repartirán en varios grupos, de modo que cada grupo tenga :@0.124841:0.639448:0.907535:0.639448:0.907535:0.623778:0.124841:0.623778:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el mismo número de integrantes. ¿De cuántas formas diferentes se puede hacer esto, si cada grupo debe :@0.124841:0.656045:0.907754:0.656045:0.907754:0.640375:0.124841:0.640375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tener más de 5, pero menos de 20 niños?:@0.124841:0.672641:0.426371:0.672641:0.426371:0.656971:0.124841:0.656971:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5. :@0.096352:0.706788:0.115093:0.706788:0.115093:0.689652:0.096352:0.689652:0.000000:0.000000:0.000000
¿Cuánto vale el área de la parte oscura?  :@0.124841:0.706788:0.420970:0.706788:0.420970:0.691118:0.124841:0.691118:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
6. :@0.096352:0.891340:0.115093:0.891340:0.115093:0.874204:0.096352:0.874204:0.000000:0.000000:0.000000
¿A qué descuento equivale dos descuentos sucesivos del 10 % y del 20 %?:@0.124841:0.891340:0.668984:0.891340:0.668984:0.875670:0.124841:0.875670:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Recuperado de: https://www.canguromat.org.es:@0.646127:0.602644:0.903641:0.602644:0.903641:0.591248:0.646127:0.591248:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.597549:0.130859:0.608388:0.130859:0.608388:0.116613:0.597549:0.116613:0.000000
C:@0.811443:0.130859:0.820992:0.130859:0.820992:0.116613:0.811443:0.116613:0.000000
M:@0.596460:0.181151:0.609493:0.181151:0.609493:0.166905:0.596460:0.166905:0.000000
N:@0.810874:0.181151:0.821562:0.181151:0.821562:0.166905:0.810874:0.166905:0.000000
A:@0.598068:0.231443:0.607868:0.231443:0.607868:0.217197:0.598068:0.217197:0.000000
B:@0.811979:0.231443:0.820439:0.231443:0.820439:0.217197:0.811979:0.217197:0.000000
A:@0.650681:0.472866:0.660481:0.472866:0.660481:0.458621:0.650681:0.458621:0.000000
C:@0.603891:0.577222:0.613440:0.577222:0.613440:0.562977:0.603891:0.562977:0.000000
B:@0.805473:0.577222:0.813933:0.577222:0.813933:0.562977:0.805473:0.562977:0.000000
D:@0.702965:0.586802:0.713804:0.586802:0.713804:0.572557:0.702965:0.572557:0.000000
H:@0.621833:0.535731:0.632387:0.535731:0.632387:0.521486:0.621833:0.521486:0.000000
α α:@0.660749:0.504304:0.692863:0.504304:0.692863:0.488759:0.660749:0.488759:0.000000:0.000000:0.000000
4:@0.701893:0.546628:0.710068:0.546628:0.710068:0.532383:0.701893:0.532383:0.000000
α:@0.710068:0.552709:0.718722:0.552709:0.718722:0.537164:0.710068:0.537164:0.000000
6:@0.473816:0.738689:0.480356:0.738689:0.480356:0.726770:0.473816:0.726770:0.000000
3:@0.474941:0.854341:0.481481:0.854341:0.481481:0.842422:0.474941:0.842422:0.000000
3:@0.602420:0.795509:0.608961:0.795509:0.608961:0.783590:0.602420:0.783590:0.000000
El área del cuadrilátero es 5 cm .:@0.211148:0.273323:0.360491:0.273323:0.360491:0.263352:0.211148:0.263352:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.355115:0.269475:0.358451:0.269475:0.358451:0.263662:0.355115:0.263662:0.000000
El área es 4 ½ cm .:@0.211151:0.439735:0.295984:0.439731:0.295984:0.429759:0.211151:0.429763:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.290608:0.435883:0.293944:0.435883:0.293944:0.430069:0.290608:0.430069:0.000000
El ángulo CAB mide 60°.:@0.211153:0.603608:0.322838:0.603608:0.322838:0.593636:0.211153:0.593636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
9:@0.420099:0.705551:0.425822:0.705551:0.425822:0.695579:0.420099:0.695579:0.000000
28 %:@0.676655:0.888728:0.699311:0.888728:0.699311:0.878757:0.676655:0.878757:0.000000:0.000000:0.000000:0.000000
El ángulo CAB mide 60°.:@0.435707:0.669906:0.547392:0.669906:0.547392:0.659935:0.435707:0.659935:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000