Circle circled circlesGeometry 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 \( M \).