KöMaL 2017 B4916

Let $P(a,b,c)$ be a fixed point in the 3D Cartesian coordinate system. Let $a,b,c>0$ and let $O$ denote the origin. Let $S$ be a plane passing through $P$ that intersects the positive coordinate axes at the points $X$, $Y$ and $Z$. Show that the volume of tetrahedron $OXYZ$ is a minimum if and only if $P$ is the centroid of triangle $XYZ\triangle$.