IMO 1985-5
Posted: Sun Feb 12, 2012 9:17 pm
A circle with center $O$ passes through points $A$ and $C$ and intersects side $AB$ and $BC$ of $\triangle ABC$ at point $K,N$,respectively.The circumcircles of $\triangle ABC$ and $\triangle KBN$ at $B$ and $M$.Prove that $\angle OMB=90^0$.