IMO Shortlist 2014 problem G1


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7. svibnja 2017.
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The points P and Q are chosen on the side BC of an acute-angled triangle ABC so that \angle PAB = \angle ACB and \angle QAC = \angle 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)

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