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# hard geometry questions :(

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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!

Apr 6, 2020

#1
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1. By power of a point, the radius is sqrt(33).

2. by power of a point, CM = 5*sqrt(3).

Apr 8, 2020