Let ABCD be an isosceles trapezoid with AD∥BC. Its diagonals AC and BD intersect at point M. Points X and Y on the segment AB are such that AX \equal{} AM, BY \equal{} BM. Let Z be the midpoint of XY and N is the point of intersection of the segments XD and YC. Prove that the line ZN is parallel to the bases of the trapezoid.
Author: A. Akopyan, A. Myakishev geometrytrapezoidanalytic geometryratioperpendicular bisectorangle bisectorprojective geometry