Math Problem Solver

Problem 2. Let ABC be a triangle inscribed in a circle ω and let I be

its incenter. Let D be the midpoint of the arc BC in ω that contains A. Let

P and Q be the intersections of the line perpendicular to AI through I with

the segments AC and AB respectively. Let R be the second intersection of the

circumcircles of the triangles BIP and CIQ. Prove that the points D, I, and

R are aligned.