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 \(CM.\)
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