IMO Shortlist 1985 problem 22

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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}.
Source: Međunarodna matematička olimpijada, shortlist 1985