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Circumcircle's Headache

Let ABC be an acute-angled triangle with AB =6 AC. The circle with diameter BC intersects the sides AB and AC at M and N, respectively. Denote by O the midpoint of 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 line segment BC.

Note by Chinmay Sangawadekar
1 year, 3 months ago

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