Question 94
Given $\triangle ABC$, let $I$, $O$, $\Gamma$ denote its incenter, circumcenter and circumcircle respectively. Let $AI$ intersect $\Gamma$ at $M\ (\neq A)$. Circle $\omega$ is tangent to $AB$, $AC$ and $\Gamma$ internally at $T$ (i.e. the mixtilinear incircle opposite $A$). Let the tangents at $A$ and $T$ to $\Gamma$ meet at $P$, and let $PI$ and $TM$ intersect at $Q$. Prove that $QA$ and $MO$ intersect at a point on $\Gamma$.