KöMaL 2014 A607

The circles $k_1$, $k_2$ and $k_3$ are pairwise externally tangent to each other; the point of tangency between $k_1$ and $k_2$ is $T$. One of the external common tangents of $k_1$ and $k_2$ meets $k_3$ at points $P$ and $Q$. Prove that the internal common tangent of $k_1$ and $k_2$ bisects the arc $PQ$ of $k_3$ which is closer to $T$.