Concurrent Lines that Intersect on the Euler Line

Abstract

The Euler line of a triangle goes through the circumcenter and the orthocenter.Let ABC be a triangle. Let O be the circumcenter and H the orthocenter of ABC. Let the intersection of AO BO and CO with the circumcircle be and respectively. Let the intersection of and with the circumcircle be A B and C respectively. Let the intersection of AH BH and CH with the circumcircle be A;