0353 tetrahedron 3rd edition Round 5 p3
Source:
May 9, 2021
3D geometrygeometry3rd editiontetrahedron
Problem Statement
We say that a tetrahedron is median if and only if for each vertex the plane that passes through the midpoints of the edges emerging from the vertex is tangent to the inscribed sphere. Also a tetrahedron is called regular if all its faces are congruent. Prove that a tetrahedron is regular if and only if it is median.