A sphere and a cube
Source: Italian National MO 1996, Problem 3
December 12, 2005
geometry3D geometrysphereanalytic geometrysymmetry
Problem Statement
Given a cube of unit side. Let and be two opposite vertex. Determine the radius of the sphere, with center inside the cube, tangent to the three faces of the cube with common point and tangent to the three sides with common point .