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

1952 Moscow Mathematical Olympiad, 210
Tags: parallelogram , rhombus , parallelepiped , 3d geometry , geometry
Prove that if all faces of a parallelepiped are equal parallelograms, they are rhombuses.

2018 District Olympiad, 3
Tags: 3d geometry , cube , parallelepiped , collinear , geometry
Let $ABCDA'B'C'D'$ be the rectangular parallelepiped. Let $M, N, P$ be midpoints of the edges $[AB], [BC],[BB']$ respectively . Let $\{O\} = A'N \cap C'M$. a) Prove that the points $D, O, P$ are collinear. b) Prove that $MC' \perp (A'PN)$ if and only if $ABCDA'B'C'D'$ is a cube.