IMO Shortlist 2017 problem G2
Let and be different points on a circle such that is not a diameter. Let be the tangent line to at . Point is such that is the midpoint of the line segment . Point is chosen on the shorter arc of so that the circumcircle of triangle intersects at two distinct points. Let be the common point of and that is closer to . Line meets again at . Prove that the line is tangent to .