Let ABC be an acute triangle with orthocenter H. The circle through B,H, and C intersects lines AB and AC at D and E respectively, and segment DE intersects HB and HC at P and Q respectively. Two points X and Y, both different from A, are located on lines AP and AQ respectively such that X,H,A,B are concyclic and Y,H,A,C are concyclic. Show that lines XY and BC are parallel. geometryorthocenterparallel