A polyhedron is circumscribed around a sphere. Let's call its face large if the projection of the sphere onto the plane of the face falls entirely within the face. Prove that there are no more than 6 large faces.
Source: - All-Russian MO 1999 Regional (R4) 11.4
Tags: geometry, 3D geometry, sphere
A polyhedron is circumscribed around a sphere. Let's call its face large if the projection of the sphere onto the plane of the face falls entirely within the face. Prove that there are no more than 6 large faces.