Question 107
Let $\Gamma$ be the circumcircle of triangle $ABC$. Let $\Gamma_A$ be the circle which is tangent to $AB$, $AC$ and tangent to $\Gamma$ internally, $\Gamma_B$ be the circle which is tangent to $AB$, $BC$ and tangent to $\Gamma$ internally, and $\Gamma_C$ be the circle which is tangent to $AC$, $BC$ and tangent to $\Gamma$ internally. Denote $\Gamma_A, \Gamma_B, \Gamma_C$ are tangent to $\Gamma$ at $P, Q, R$. Prove that the lines $AP, BQ, CR$ are concurrent.