# Circle circled circles

Geometry Level 4

Let $$AB$$ be the diameter of circle $$\Gamma_1$$. In the interior of $$\Gamma_1$$, there are circles $$\Gamma_2$$ and $$\Gamma_3$$ that are tangent to $$\Gamma_1$$ at $$A$$ and $$B$$, respectively. $$\Gamma_2$$ and $$\Gamma_3$$ are also externally tangent at the point $$C$$. This tangent line (at $$C$$) cuts $$\Gamma_1$$ at $$P$$ and $$Q$$, with $$PQ = 20$$. The area that is within $$\Gamma_1$$ but not in $$\Gamma_2$$ or $$\Gamma_3$$ is equal to $$M\pi$$. Determine $$M$$.

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