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: 2

1998 Tuymaada Olympiad, 4
Tags: plane , dissecting plane , 3d geometry , solid geometry , geometry , tetrahedron
Given the tetrahedron $ABCD$, whose opposite edges are equal, that is, $AB=CD, AC=BD$ and $BC=AD$. Prove that exist exactly $6$ planes intersecting the triangular angles of the tetrahedron and dividing the total surface and volume of this tetrahedron in half.

2011 Sharygin Geometry Olympiad, 18
Tags: combinatorial geometry , geometry , line , dissecting plane
On the plane, given are $n$ lines in general position, i.e. any two of them aren’t parallel and any three of them don’t concur. These lines divide the plane into several parts. What is a) the minimal, b) the maximal number of these parts that can be angles?