Let ABC be a fixed triangle. Point D is an arbitrary point on the side BC. Point P is fixed on AD. The circumcircle of triangle BPD meets AB at E distinct from B. Point Q varies on AP. Let BQ and CQ meet the circumcircles of triangles BPD,CPD respectively at F,Z distinct from B,C. Prove that the circumcircle EFZ is through a fixed point distinct from E and this fixed point is on the circumcircle of triangle CPD.Kostas Vittas geometryfixedFixed pointcircumcircle