Problem

Source: Polish Junior Math Olympiad 2nd Round 2020

Tags: geometry, parallelogram, perpendicular bisector



Let ABCD be the parallelogram, such that angle at vertex A is acute. Perpendicular bisector of the segment AB intersects the segment CD in the point X. Let E be the intersection point of the diagonals of the parallelogram ABCD. Prove that XE=12AD.