# 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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