MathDB

2

Part of 2012 Cuba MO

Problems(2)

in a school with 5 different grades there are 250 girls and 250 boys

Source: 2012 Cuba MO 1.2

9/18/2024
In a school with 5 different grades there are 250 girls and 250 boys. Each grade has the same number of students. for a competition of knowledge wants to form teams of a female and a male who are of the same grade. If in each grade there are at least 1919 females and 1919 males. Find the greatest amount of teams that can be formed.
combinatorics
CP//BQ , midpoints, 2012 Cuba MO 2.2

Source:

9/18/2024
Given the triangle ABCABC, let LL, MM and NN be the midpoints of BCBC, CACA and ABAB respectively. The lines LMLM and LNLN cut the tangent to the circumcircle at AA at PP and QQ respectively . Prove that CP∥BQCP \parallel BQ.
geometryparallel