MathDB

G4

Part of 2013 IMO Shortlist

Problems(1)

IMO Shortlist 2013, Geometry #4

Source: IMO Shortlist 2013, Geometry #4

7/10/2014
Let ABCABC be a triangle with ∠B>∠C\angle B > \angle C. Let PP and QQ be two different points on line ACAC such that ∠PBA=∠QBA=∠ACB\angle PBA = \angle QBA = \angle ACB and AA is located between PP and CC. Suppose that there exists an interior point DD of segment BQBQ for which PD=PBPD=PB. Let the ray ADAD intersect the circle ABCABC at R≠AR \neq A. Prove that QB=QRQB = QR.
geometrycircumcircleIMO Shortlistgeometry solvedIsosceles TriangleAngle ChasingInversion