Let ABC be an acute triangle and D be an intersection of the angle bisector of A and side BC. Let Ω be a circle tangent to the circumcircle of triangle ABC and side BC at A and D, respectively. Ω meets the sides AB,AC again at E,F, respectively. The perpendicular line to AD, passing through E,F meets Ω again at G,H, respectively. Suppose that AE and GD meet at P, EH and GF meet at Q, and HD and AF meet at R. Prove that QGQF=PGHR. geometryangle bisectorcircumcircle