KöMaL 2006 A392

The inradius of a tetrahedron is $r$. There exists three spheres which touch the four face planes such that all touching points are outside the surface of the tetrahedron; the radii of those spheres are $r_1$, $r_2$ and $r_3$. Show that $r_1$+$r_2$+$r_3$>9$r$.