Problem

Source: Tuymaada 2008, Junior League, Second Day, Problem 6.

Tags: geometry, trapezoid, analytic geometry, ratio, perpendicular bisector, angle bisector, projective geometry



Let ABCD be an isosceles trapezoid with ADBC. Its diagonals AC and BD intersect at point M. Points X and Y on the segment AB are such that AX=AM, BY=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