Let ABC be an acute angled triangle with circumcircle O. Line AO intersects the circumcircle of triangle ABC again at point D. Let P be a point on the side BC. Line passing through P perpendicular to AP intersects lines DB and DC at E and F respectively . Line passing through D perpendicular to BC intersects EF at point Q. Prove that EQ=FQ if and only if BP=CP. geometryequal segmentscircumcircleperpendicular