Let ABC be a triangle inscribed in a circle (O). Let P be an arbitrary point in the plane of triangle ABC. Points A′,B′,C′ are the reflections of P about the lines BC,CA,AB respectively. X is the intersection, distinct from A, of the circle with diameter AP and the circumcircle of triangle AB′C′. Points Y,Z are defined in the same way. Prove that five circles (O),(AB′C′), (BC′A′),(CA′B′),(XYZ) have a point in common.Nguyễn Văn Linh concurrentconcurrent circlescirclesgeometry