hard geometry questions :(

I came across these tough problems and have no idea how to solve them. Help would be appreciated.

1. In the diagram below, $\overline{PQ}$ is tangent at $P$ to the circle with center $O$, point $S$ is inside the circle, and $\overline{QS}$ intersects the circle at $R$. If $QR = RS = 3$, $OS = 2$ , and $PQ = 6$, then find the radius of the circle.

2. In right triangle $ABC$, the length of side $\overline{AC}$ is $8$, the length of side $\overline{BC}$ is $6,$ and $\angle C = 90^\circ.$ The circumcircle of triangle $ABC$ is drawn. The angle bisector of $\angle ACB$ meets the circumcircle at point $M.$ Find the length $CM$.

Thanks a lot!