IMO Shortlist 2004 problem G1


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2. travnja 2012.
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1. Let ABC be an acute-angled triangle with AB\neq AC. The circle with diameter BC intersects the sides AB and AC at M and N respectively. Denote by O the midpoint of the side BC. The bisectors of the angles \angle BAC and \angle MON intersect at R. Prove that the circumcircles of the triangles BMR and CNR have a common point lying on the side BC.
Izvor: Međunarodna matematička olimpijada, shortlist 2004