MathDB

ASU 486 All Soviet Union MO 1988 r < ab/( 2(a + b) ) inradius of tetrahedron

Source:

August 8, 2019

spheretetrahedronradicalgeometric inequality3D geometrygeometry

Problem Statement

Prove that for any tetrahedron the radius of the inscribed sphere

r <\frac{ ab}{ 2(a + b)}

, where

a

and

b

are the lengths of any pair of opposite edges.