International Mathematical Olympiad 1985 Problem 5

A circle with center $O$ passes through the vertices $A$ and $C$ of triangle $ABC$ and intersects the segments $AB$ and $BC$ again at distinct points $K$ and $N$, respectively. The circumscribed circles of the triangles $ABC$ and $EBN$ intersect at exactly two distinct points $B$ and $M$. Prove that angle OMB is a right angle.