Let K be a point inside an acute triangle ABC, such that BC is a common tangent of the circumcircles of AKB and AKC. Let D be the intersection of the lines CK and AB, and let E be the intersection of the lines BK and AC . Let F be the intersection of the line BC and the perpendicular bisector of the segment DE. The circumcircle of ABC and the circle k with centre F and radius FD intersect at points P and Q.
Prove that the segment PQ is a diameter of k. geometrycircumcircletrigonometrygeometric transformationreflectionperpendicular bisectorpower of a point