Show that the tetrahedron is regular
Source: ARMO 1997, 11.7
April 20, 2013
geometry3D geometrytetrahedronsphere
Problem Statement
A sphere inscribed in a tetrahedron touches one face at the intersection of its angle bisectors, a second face at the intersection of its altitudes, and a third face at the intersection of its medians. Show that the tetrahedron is regular.
N. Agakhanov