11.4

Part of 1999 All-Russian Olympiad Regional Round

Problems(1)

circumscribed polyhedron around a sphere has <= 6 large faces

Source: - All-Russian MO 1999 Regional (R4) 11.4

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.

geometry3D geometrysphere