Online Geometry Problem 781: Triangle, Orthocenter, Circumcenter, Circle,
Vertex, Altitude, Midpoint, Perpendicular. Level: High School, College,
Mathematics Education

The figure below shows a triangle ABC with the
orthocenter H and the circumcenter O. If M is the midpoint of BH and DE
is perpendicular to OM at M, prove that M is the midpoint of DE.