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# few geometry questions

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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!

Apr 5, 2020

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1. By power of a point, the radius is 3*sqrt(2).

2. By power of a point, CM = 4*sqrt(3).

Apr 5, 2020
#2
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Those answers were incorrect. Do you have any other methods?

Apr 5, 2020