KöMaL 2013 A597

The circles $k_0$, $k_1$, $k_2$, $k_3$ and $k_4$ lie in the plane in such a way that for $i$=1,2,3,4 the circle $k_i$ is externally tangent to $k_0$ at point $T_i$, and $k_i$ is externally tangent to $k_{i+1}$ at point $S_i$ ($k_5$=$k_1$). Let $O$ be the center of $k_0$. Let the lines $T_1 T_3$ and $T_2 T_4$ meet at $T$, and let the lines $S_1 S_3$ and $S_2 S_4$ meet at $S$. Prove that the points $O$, $T$ and $S$ are collinear.