Let ABC be a triangle with circumcircle ω and circumcenter O. The tangent line to from A to ω intersects BC at K. The tangent line to from B to ω intersects AC at L. Let M,N be the midpoints of AK,BL respectively. The line MN is named by α. The feet of perpendicular from A,B,C to the edges of △ABC are named by D,E,F respectively. The perpendicular bisectors of EF,DF,DE intersect α at X,Y,Z respectively. Let AD,BE,CF intersect ω again at D′,E′,F′ respectively. If H is the orthocenter of ABC, prove that the lines XD′,YE′,ZF′,OH are concurrent. geometrycircumcircleEulerperpendicular bisector