Question 58
Let $ABCD$ be a trapezium with acute angles along the base $\overline{AB}$ and perpendicular diagonals which intersect at $O$. Ray $OA$ intersects the circle with diameter $\overline{BD}$ at $M$, and ray $OB$ intersects the circle with diameter $\overline{AC}$ at $N$. Prove that the points $M$, $N$, $C$ and $D$ lie on the same circle. (New Zealand 2012)