IMO 2014 Shortlist G3
Let Ω and O be the circumcircle and the circumcentre of an acute-angled triangle ABC with AB ą BC. The angle bisector of...
Category: Geometry
Problem
Let Ω and O be the circumcircle and the circumcentre of an acute-angled triangle ABC with AB ą BC. The angle bisector of =ABC intersects Ω at M ‰ B. Let Γ be the circle with diameter BM. The angle bisectors of =AOB and =BOC intersect Γ at points P and Q, respectively. The point R is chosen on the line PQ so that BR “ MR. Prove that BR k AC. (Here we always assume that an angle bisector is a ray.) (Russia)