IMO Shortlist 2014 problem G3


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7. svibnja 2017.
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Let \Omega and O be the circumcircle and the circumcentre of an acute-angled triangle ABC with AB > BC. The angle bisector of \angle ABC intersects \Omega at M \neq B. Let \Gamma be the circle with diameter BM. The angle bisectors of \angle AOB and \angle BOC intersect \Gamma at points P and Q, respectively. The point R is chosen on the line PQ so that BR = MR. Prove that BR \parallel AC. (Here we always assume that an angle bisector is a ray.)

(Russia)

Izvor: https://www.imo-official.org/problems/IMO2014SL.pdf