a) Find the locus of centroids for triangles whose vertices lie on the sides of a given triangle (each side contains a single vertex). b) Find the locus of centroids for tetrahedrons whose vertices lie on the faces of a given tetrahedron (each face contains a single vertex).
Problem
Source: 2011 Sharygin Geometry Olympiad Correspondence Round P13
Tags: Locus, geometry, Centroid, inscribed triangle, tetrahedron, 3D geometry