This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 27

2018 Singapore Senior Math Olympiad, 2
Tags: geometry , parallel , similar , similar triangles
In a convex quadrilateral $ABCD, \angle A < 90^o, \angle B < 90^o$ and $AB > CD$. Points $P$ and $Q$ are on the segments $BC$ and $AD$ respectively. Suppose the triangles $APD$ and $BQC$ are similar. Prove that $AB$ is parallel to $CD$.

1940 Eotvos Mathematical Competition, 3
Tags: triangle inequality , similar , median , geometry
(a) Prove that for any triangle $H_1$, there exists a triangle $H_2$ whose side lengths are equal to the lengths of the medians of $H_1$. (b) If $H_3$ is the triangle whose side lengths are equal to the lengths of the medians of $H_2$, prove that $H_1$ and $H_3$ are similar.