IMO 2014 Shortlist G1

The points P and Q are chosen on the side BC of an acute-angled triangle ABC so that =PAB “ =ACB and =QAC “ =CBA. The po...

IMO 2014 Shortlist G1

Category: Geometry

Problem

The points P and Q are chosen on the side BC of an acute-angled triangle ABC so that =PAB “ =ACB and =QAC “ =CBA. The points M and N are taken on the rays AP and AQ, respectively, so that AP “ PM and AQ “ QN. Prove that the lines BM and CN intersect on the circumcircle of the triangle ABC. (Georgia)