MathNet 2007-part-03 — 185 problems (EN–VI) Question 34

Five distinct points $A, M, B, C$ and $D$ lie on a circle $k$ in this order, and $MA = MB$. The lines $AC$ and $MD$ meet at $P$, and the lines $BD$ and $MC$ meet at $Q$. The line $PQ$ meets $k$ at $X$ and $Y$. Show that $MX = MY$.