Prove that if a regular icosahedron and a regular dodecahedron have a common circumsphere, then they have a common insphere. (7 points)
Source: Spring 2005 Tournament of Towns Senior A-Level #5
Tags: geometry, 3D geometry
Prove that if a regular icosahedron and a regular dodecahedron have a common circumsphere, then they have a common insphere. (7 points)