The Fuhrmann Circle
Let ABC be a triangle. Let A', B', and C' be the midpoints of the arcs BC, AC, and AB on the circumcircle. Let A'', B'', and C'' be the reflections of A', B', and C' across the sides of the triangle. Then A'', B'', C'', the orthocenter H, and the Nagel point N all lie on a circle (called the Fuhrmann circle).