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A circle is centered at $O.$ The tangent to the circle at $P$ is extended to $Q.$ Line segment $\overline{QS}$ intersects the circle at $R.$ Given that $OS = 2,$ $SR = RQ = 3$, and $PQ = 6$, find the radius of the circle.

 

[asy] unitsize(2 cm); pair A, B, C, D, E, F, G, O; A = dir(70); B = A + 1.2*dir(-20); C = dir(25); D = 2*C - B; O = (0,0); draw(Circle(O,1)); draw(A--B--D--O); dot("$P$", A, N); dot("$Q$", B, dir(0)); dot("$R$", C, SW); dot("$S$", D, NW); dot("$O$", O, SW); [/asy]

 Aug 14, 2020
 #1
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Image Here:

 

 Aug 15, 2020
 #2
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By power of a point, the radius of the circle is 4*sqrt(7).

 Aug 15, 2020
 #3
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Maybe it would be in your interest to present your questions better.

 

All those unnecessary dollar signs make it difficult to read and I feel that if you cannot be bothered to present your question properly then it is not worth my effort to attempt to answer.  

 Aug 15, 2020

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