2015 IMO Problems/Problem 3
Let be an acute triangle with . Let be its circumcircle, its orthocenter, and the foot of the altitude from . Let be the midpoint of . Let be the point on such that $\angle HKQ=90 \degree$ (Error compiling LaTeX. ! Undefined control sequence.). 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.