Online Geometry Problem 783: Triangle, Orthocenter, Circumcenter,
Circumcircle,
Diameter, Altitude, Midpoint. Level: High School, College,
Mathematics Education

The figure below shows a triangle ABC with the
orthocenter H and the circumcenter O. If AD is the diameter of the
circumcircle O, and DH meet BC at M, prove that M is the midpoint of DH
and BC.