KöMaL 2013 A581

In the plane, there are given two circles $k_1$ and $k_2$ with different radii, and a point $O$ lying outside the circles. The end-points of the tangents drawn from $O$to $k_1$ are $P$ and $Q$, the end-points of the tangents drawn from $O$ to $k_2$ are $R$ and $S$. The points $P$, $Q$, $R$, $S$ are distinct. Let $H$ be the external homothety center between $k_1$ and $k_2$. Prove that if $PR$ is not a external common tangent to the circles but passes through $H$ then $QS$ also passes through $H$.