IMO 2013 Shortlist G4

Let ABC be a triangle with =B ą =C. Let P and Q be two different points on line AC such that =PBA “ =QBA “ =ACB and A is...

IMO 2013 Shortlist G4

Category: Geometry

Problem

Let ABC be a triangle with =B ą =C. Let P and Q be two different points on line AC such that =PBA “ =QBA “ =ACB and A is located between P and C. Suppose that there exists an interior point D of segment BQ for which PD “ PB. Let the ray AD intersect the circle ABC at R ‰ A. Prove that QB “ QR. (Georgia)