Question 42
Let $AB$ be a chord of a circle $\Omega$ with centre $M$, and $P$ a point on the segment $AB$. Circles $\Omega_A$ and $\Omega_B$ pass through $P$ and are tangent to $\Omega$ at $A$ and $B$, respectively. Let $Q$ be the second intersection point of $\Omega_A$ and $\Omega_B$. Prove that $\angle PQM$ is a right angle.