Geometry Problem 1248

Elements: Triangle, Circumcircle, Circle, Diameter, Orthocenter, Altitude, Parallel Lines

A triangle ABC with orthocenter H and altitudes AD, BF, and CE is inscribed in a circle O (see the figure below). DE cuts BF at G and the diameter BK cuts AC at M. Prove that HK and GM are parallel.


Geometry Problem 1248: Triangle, Circumcircle, Circle, Diameter, Orthocenter, Altitude, Parallel Lines