Geometry Problem 1247

Elements: Triangle, Circumcircle, Orthocenter, Altitude, Perpendicular, Midpoint

A triangle ABC with orthocenter H is inscribed in a circle O and a point D is on arc AC. DE is perpendicular to BC and DF is perpendicular to AC. EF cuts DH at M. (See the figure below). Prove that M is the midpoint of DH.


Geometry Problem 1247: Triangle, Circumcircle, Orthocenter, Altitude, Perpendicular, Midpoint