Geometry Problem 1385: Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, Midpoint, Collinear Points

Proposition

The figure below shows a triangle ABC so that H is the orthocenter, BD is the internal bisector, and M is the midpoint of AC. Line EHF is perpendicular to BD. The circumcircle of the triangle BEF cuts the circumcircle of the triangle ABC and BD at G and N, respectively. Prove that the points G, H, N, and M are collinear.
 

Geometry Problem 1385: Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, Midpoint, Collinear Points
 

See also
Conformal Mapping or Transformation of Problem 1382

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