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

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Found problems: 2

1935 Moscow Mathematical Olympiad, 009
The height of a truncated cone is equal to the radius of its base. The perimeter of a regular hexagon circumscribing its top is equal to the perimeter of an equilateral triangle inscribed in its base. Find the angle $\phi$ between the cone’s generating line and its base.
cone hexagon geometry 3d geometry angle regular hexagon solid geometry

1937 Moscow Mathematical Olympiad, 036
* Given a regular dodecahedron. Find how many ways are there to draw a plane through it so that its section of the dodecahedron is a regular hexagon?
dodecahedron geometry 3d geometry plane combinatorics combinatorial geometry regular hexagon solid geometry