KöMaL 2021 B5171

Let $OLMN$ be a tetrahedron, and the vertices $A$, $B$ and $C$ of another tetrahedron $OABC$ lie on the rays $OL$, $OM$ and $ON$, respectively. The centre of the inscribed circle of triangle $LMN$ coincides with the centroid of triangle $ABC$. Show that the volume of tetrahedron $OLMN$ is greater than or equal to the volume of tetrahedron $OABC$. On what condition will the volumes of the two tetrahedra be equal?