Let ABC be a non-equilateral triangle in the plane, and let T be a point different from its vertices. Define AT, BT and CT as the points where lines AT, BT, and CT meet the circumcircle of ABC. Prove that there are exactly two points P and Q in the plane for which the triangles APBPCP and AQBQCQ are equilateral. Prove furthermore that line PQ contains the circumcenter of △ABC. geometrycircumcirclegeometry unsolved