sum of edges of 4 tetrahedra equals sum of edges of another tetrahedron
Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1998 p3
February 20, 2020
geometry3D geometryspheretetrahedron
Problem Statement
A sphere is inscribed in a tetrahedron . The tangent planes to the sphere parallel to the faces of the tetrahedron cut off four smaller tetrahedra. Prove that sum of all the edges of the smaller tetrahedra equals twice the sum of edges of the tetrahedron .