NL-NWO 1984 Problem 1

The circles $C_1$ and $C_2$ with radii $r_1$ and $r_2$ touch the line $p$ at the point $P$ . $C_1$ lies entirely within $C_2$ . Line $q \perp p$ intersects $p$ at $S$ and touches $C_1$ at $R$ . $q$ intersects $C_2$ at $M$ and $N$ , where $N$ is between $R$ and $S$ . a) Prove that line $PR$ bisects angle $\angle MPN$ . b) Calculate the ratio $r_1 : r_2$ if line $PN$ bisects angle $\angle RPS$ .