MMO 203 Moscow MO 1951 sphere inscribed in n-angled pyramid.
Source:
August 7, 2019
geometry3D geometryspherepyramid
Problem Statement
A sphere is inscribed in an -angled pyramid. Prove that if we align all side faces of the pyramid with the base plane, flipping them around the corresponding edges of the base, then
(1) all tangent points of these faces to the sphere would coincide with one point, , and
(2) the vertices of the faces would lie on a circle centered at .