Question 22
(USS 5), IMO5. A circle with center $O$ passes through points $A$ and $C$ and intersects the sides $AB$ and $BC$ of the triangle $ABC$ at points $K$ and $N$, respectively. The circumscribed circles of the triangles $ABC$ and $KBN$ intersect at two distinct points $B$ and $M$. Prove that $\angle OMB=90^\circ$.