Math Trek: Math Olympiad in Athens, Science News Online, Aug. 7, 2004

“Let ABC be an acute-angled triangle with AB not equal to 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 BAC and MON intersect at R. Prove that the circumcircles of the triangles BMR and CNR have a common point lying on the side BC.”

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