11.8

Part of VI Soros Olympiad 1999 - 2000 (Russia)

Problems(1)

plane that bisects both surface area and volume

Source: VI Soros Olympiad 1999-00 Round 1 11.8 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

Prove that the plane dividing in equal proportions the surface area and volume of the circumscribed polyhedron passes through the center of the sphere inscribed in this polyhedron.

geometry3D geometrybisectsVolume