Question 110
Let $ABC$ be an acute triangle and $M$ is the midpoint of $AB$. A circle through the vertices $B$ and $C$ intersects the segments $CM$ and $BM$ in points $P$ and $Q$ respectively. Let $K$ be symmetrical point to $P$ regarding $M$. Let circumcircles of $\triangle AKM$ and $\triangle CQM$ meet again in point $X$, and circumcircles of $\triangle AMC$ and $\triangle KMQ$ meet again in point $Y$. The segments $BP$ and $CQ$ meet in $T$. Prove that $MT$ is tangent to the circumcircle of $\triangle MXY$.