IMO Shortlist 2013 problem G4

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Dodao/la: arhiva
21. rujna 2014.
Let ABC be a triangle with \angle B > \angle C. Let P and Q be two different points on line AC such that \angle PBA = \angle QBA = \angle ACB and A is located between P and C. Suppose that there exists and interior point D of segment BQ for which PD = PB. Let the ray AD intersect the circle ABC at R \neq A. Prove that QB = QR.
Izvor: Georgia