Online Geometry Problem 784: Triangle, Orthocenter, Altitude, Midpoint of a side,
Perpendicular. Level: High School, College,
Mathematics Education

The figure below shows a triangle ABC with the
orthocenter H. M is the midpoint of BC and EF
is perpendicular to MH at H (E on AB, F on AC extended). Prove that H is the midpoint of
EF.