4

Part of 1994 Tuymaada Olympiad

Problems(1)

arranging a ball inside of a convex polyhedron

Source: Tuymaada 1994 p4

Let a convex polyhedron be given with volume

V

and full surface

S

. Prove that inside a polyhedron it is possible to arrange a ball of radius

\frac{V}{S}

geometryconvexpolyhedronsphere