In an acute triangle ABC with AB<AC, angle bisector of A and perpendicular bisector of BC intersect at D. Let P be an interior point of triangle ABC. Line CP meets the circumcircle of triangle ABP again at K. Prove that B,D,K are collinear if and only if AD and BC meet on the circumcircle of triangle APC. geometryangle bisectorperpendicular bisectorcircumcircle