Show that R / r > a / h in any triangular pyramid ABCD
Source: Tournament of Towns Spring 2003 - Senior A-Level - Problem 1
June 15, 2011
geometry3D geometrypyramidspheregeometry unsolved
Problem Statement
A triangular pyramid is given. Prove that , where is the radius of the circumscribed sphere, is the radius of the inscribed sphere, is the length of the longest edge, is the length of the shortest altitude (from a vertex to the opposite face).