Let ABCD be a cyclic quadrilateral. Let DA and BC intersect at E and let AB and CD
intersect at F. Assume that A,E,F all lie on the same side of BD. Let P be on segment DA
such that ∠CPD=∠CBP, and let Q be on segment CD such that ∠DQA=∠QBA. Let AC and PQ meet at X. Prove that, if EX=EP, then EF is perpendicular to AC. cyclic quadrilateralRMM ShortlistgeometryHybrid