IMO 2015 Shortlist G6
Let ABC be an acute triangle with AB ą AC, and let Γ be its circumcircle. Let H, M, and F be the orthocenter of the tria...
Category: Geometry
Problem
Let ABC be an acute triangle with AB ą AC, and let Γ be its circumcircle. Let H, M, and F be the orthocenter of the triangle, the midpoint of BC, and the foot of the altitude from A, respectively. Let Q and K be the two points on Γ that satisfy =AQH “ 900 and =QKH “ 900 . Prove that the circumcircles of the triangles KQH and KFM are tangent to each other. (Ukraine)