IMO Shortlist 2014 problem G6
Let be a fixed acute-angled triangle. Consdeir some points and lying on the sides and , respecitvely, and let be the midpoint of . Let the perpendicular bisector of intersect the line at , and let the perpendicular bisector of intersect the lines and ant and , respectively. We call the pair interesting, the quadrilateral is cyclic.
Suppose that the pairs and are interesting. Prove that