IMO 2007 Shortlist G1
In triangle ABC, the angle bisector at vertex C intersects the circumcircle and the per- pendicular bisectors of sides B...
Category: Geometry
Problem
In triangle ABC, the angle bisector at vertex C intersects the circumcircle and the per- pendicular bisectors of sides BC and CA at points R, P, and Q, respectively. The midpoints of BC and CA are S and T, respectively. Prove that triangles RQT and RPS have the same area. (Czech Republic)