IMO Shortlist 1985 problem 22
Dodao/la:
arhiva2. travnja 2012. A circle with center

passes through the vertices

and

of the triangle

and intersects the segments

and

again at distinct points

and

respectively. Let

be the point of intersection of the circumcircles of triangles

and

(apart from

). Prove that

.
%V0
A circle with center $O$ passes through the vertices $A$ and $C$ of the triangle $ABC$ and intersects the segments $AB$ and $BC$ again at distinct points $K$ and $N$ respectively. Let $M$ be the point of intersection of the circumcircles of triangles $ABC$ and $KBN$ (apart from $B$). Prove that $\angle OMB=90^{\circ}$.
Izvor: Međunarodna matematička olimpijada, shortlist 1985