Let Circles $C_1$ (center $O_1$) and $C_2$ (center $O_2$) intersect at points $P$ and $Q$. $O_2$ is outside of $C_1$, $O_1$ is outside of $C_2$. Let $O_1P$ intersect $C_2$ at $R$ and $O_2P$ intersect $C_1$ at $S$. Prove that the points $R$, $S$, $O_1$, $O_2$ lie on the same circle.
Proving that the quadrilateral $O_1SRO_2$ can be inscribed in a circle seems like the next logical step, but I am having difficulties.