IMO Shortlist 2014 problem G7
Let be a triangle with circumcircle and incentre . Let the line passing through and perpendicular to intersect the segment and the arc (not containing ) of at points and , respectively. Let the line passing through and parallel to intersect at , and let the line passing through and parallel to intersect at . Let and be the midpoints of and , respectively. Prove that if the points , , and are collinear, then the points , , and are also collinear.