A triangular pyramid $ABCD$ is given. Prove that $\frac Rr > \frac ah$, where $R$ is the radius of the circumscribed sphere, $r$ is the radius of the inscribed sphere, $a$ is the length of the longest edge, $h$ is the length of the shortest altitude (from a vertex to the opposite face).
Problem
Source: Tournament of Towns Spring 2003 - Senior A-Level - Problem 1
Tags: geometry, 3D geometry, pyramid, sphere, geometry unsolved