Let ABCD be a cyclic quadrilateral inscirbed in circle O. Let the tangent to O at A meet BC at S, and the tangent to O at B meet CD at T. Circle with S as its center and passing A meets BC at E, and AE meets O again at F(=A). The circle with T as its center and passing B meets CD at K. Let P=BK∩AC. Prove that P,F,D are collinear if and only if AB=AP. geometryequal segmentscollinearcollinearitycirclescyclic quadrilateral