A sphere of radius $r$ can be inscribed in a tetrahedron. The distances between the centroid of the tetrahedron and its four faces are $w, x, y$ and $z$. Prove that $wxyz \ge r^4$. by @pepemaths .
Problem
Source: 2020 Instagram Math Olympiad R1 p6 IGMO - Shortlist g6
Tags: geometry, 3D geometry, sphere, tetrahedron, geometric inequality