Problem

Source: 2009 USAMO problem 1

Tags: geometry, analytic geometry, circumcircle, symmetry, parameterization, USAMO, 2009 USAMO



Given circles ω1 and ω2 intersecting at points X and Y, let 1 be a line through the center of ω1 intersecting ω2 at points P and Q and let 2 be a line through the center of ω2 intersecting ω1 at points R and S. Prove that if P,Q,R and S lie on a circle then the center of this circle lies on line XY.