KöMaL 2014 B4631

The circles $k_0$, $k_1$, $k_2$, $k_3$ lie in the same plane and pairwise touch each other on the outside. The point of contact of $k_i$ and $k_j$ is $T_{ij}$. Let $k_0$ have centre $O$ and radius $r$ , and let the circle $T_{12}T_{23}T_{31}$ have centre $U$ and radius $R$ . Prove that $OU^2 = R^2-4Rr+r^2$.