Question 85
Let $ABC$ be a triangle. Circle $\Omega$ passes through points $B$ and $C$. Circle $\omega$ is tangent internally to $\Omega$ and also to sides $AB$ and $AC$ at $T$, $P$, and $Q$, respectively. Let $M$ be midpoint of $\operatorname{arc} \widehat{BC}$ (containing $T$) of $\Omega$. Prove that lines $PQ$, $BC$, and $MT$ are concurrent.