CAPS 2020 Problem 1

Let $ABCD$ be a parallelogram whose diagonals meet at $P$ . Denote by $M$ the midpoint of $AB$ . Let $Q$ be a point such that $QA$ is tangent to the circumcircle of $MAD$ and $QB$ is tangent to the circumcircle of $MBC$ . Prove that points $Q,M,P$ are collinear.

(Patrik Bak, Slovakia)