Geometry Problem 1384: Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, 90 Degree

Proposition

The figure below shows a triangle ABC with the orthocenter H and the internal bisector BD. Line EHF is perpendicular to BD. The circumcircle of the triangle BEF cuts the circumcircle of the triangle ABC at G. Prove that the measure of angle HGB is 90 degrees.
 

Geometry Problem 1384: Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, 90 Degree
 

See also
Art of problem 1384
Conformal Mapping or Transformation of Problem 1382