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!
