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

1993 Czech And Slovak Olympiad IIIA, 6
Tags: combinatorial geometry , 3d geometry , tetrahedron , similar , congruent
Show that there exists a tetrahedron which can be partitioned into eight congruent tetrahedra, each of which is similar to the original one.

1940 Eotvos Mathematical Competition, 3
Tags: geometry , similar , median , triangle inequality
(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.