Let ABC be an acute-angled triangle with AC<BC. A circle passes through A and B and crosses the segments AC and BC again at A1 and B1 respectively. The circumcircles of A1B1C and ABC meet each other at points P and C. The segments AB1 and A1B intersect at S. Let Q and R be the reflections of S in the lines CA and CB respectively. Prove that the points P, Q, R, and C are concyclic. geometrycircumcirclegeometric transformationreflection