MathNet 2010 — Part 02 Question 137

As seen in Fig. 1.1, the circumcenter of acute triangle $ABC$ is $O$, $K$ is a point (not the midpoint) on the side $BC$, $D$ is a point on the extended line of segment $AK$, lines $BD$ and $AC$ intersect at point $N$, and lines $CD$ and $AB$ intersect at point $M$. Prove if $OK \perp MN$, then $A$, $B$, $D$, $C$ are concyclic.



Fig. 1.1