Samir's circle

Geometry Level 4

Let \(\Gamma\) be a circle with points \(A\) and \(B\) on the circumference. Let \(P\) be a point outside of \(\Gamma\) such that \(AP\) and \(BP\) are both tangent to the circle. Given that \(AP=6\) and \(AB=11\), the radius of \(\Gamma\) can be expressed in the form \(\frac{a\sqrt{b}}{c}\), where \(b\) is square-free, and \(a\) and \(c\) are coprime integers. What is the value of \(a+b+c\)?

This problem is posed by Samir K.

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