OMM 2012 Problem 1

Let $\mathcal{C}_1$ be a circumference with center $O$ , $P$ a point on it and $\ell$ the line tangent to $\mathcal{C}_1$ at $P$ . Consider a point $Q$ on $\ell$ different from $P$ , and let $\mathcal{C}_2$ be the circumference passing through $O$ , $P$ and $Q$ . Segment $OQ$ cuts $\mathcal{C}_1$ at $S$ and line $PS$ cuts $\mathcal{C}_2$ at a point $R$ diffferent from $P$ . If $r_1$ and $r_2$ are the radii of $\mathcal{C}_1$ and $\mathcal{C}_2$ respectively, Prove $$\frac{PS}{SR} = \frac{r_1}{r_2}.$$