MathDB
IMO Shortlist 2014 G3

Source:

July 11, 2015
geometryangle bisectorIMO Shortlist

Problem Statement

Let Ω\Omega and OO be the circumcircle and the circumcentre of an acute-angled triangle ABCABC with AB>BCAB > BC. The angle bisector of ∠ABC\angle ABC intersects Ω\Omega at M≠BM \ne B. Let Γ\Gamma be the circle with diameter BMBM. The angle bisectors of ∠AOB\angle AOB and ∠BOC\angle BOC intersect Γ\Gamma at points PP and Q,Q, respectively. The point RR is chosen on the line PQP Q so that BR=MRBR = MR. Prove that BR∥ACBR\parallel AC. (Here we always assume that an angle bisector is a ray.)
Proposed by Sergey Berlov, Russia
Back to ProblemsView on AoPS