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.