IMO Shortlist 2015 problem G6
Let be an acute triangle with . Let be its cirumcircle, its orthocenter, and the foot of the altitude from . Let be the midpoint of . Let be the point on such that and let be the point on such that . Assume that the points , , , and are all different and lie on in this order.
Prove that the circumcircles of triangles and are tangent to each other.