The Refelctions of a Line Through the Orthocenter

Take any line through the orthocenter H of the triangle (drag point E). Reflect this line in the sides of the triangle. The reflections are concurrent at a point (F) on the circumcircle. Take this point F and reflect it in the side of the triangle. Its reflections lie on the give line through the orthocenter. This is a theorem attributed to Collings and Longuet-Higgins.