IMO 2009 Shortlist G2

Let ABC be a triangle with circumcenter O. The points P and Q are interior points of the sides CA and AB, respectively. ...

IMO 2009 Shortlist G2

Category: Geometry

Problem

Let ABC be a triangle with circumcenter O. The points P and Q are interior points of the sides CA and AB, respectively. The circle k passes through the midpoints of the segments BP, CQ, and PQ. Prove that if the line PQ is tangent to circle k then OP = OQ.