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

2019 District Olympiad, 3
Tags: 3d geometry , geometry , parallelepiped , angle
Consider the rectangular parallelepiped $ABCDA'B'C'D' $ as such the measure of the dihedral angle formed by the planes $(A'BD)$ and $(C'BD)$ is $90^o$ and the measure of the dihedral angle formed by the planes $(AB'C)$ and $(D'B'C)$ is $60^o$. Determine and measure the dihedral angle formed by the planes $(BC'D)$ and $(A'C'D)$.

1995 All-Russian Olympiad Regional Round, 11.2
Tags: 3d geometry , cube , geometry , parallelepiped
A planar section of a parallelepiped is a regular hexagon. Show that this parallelepiped is a cube.