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Geometry Problem 1147: Scalene Triangle, Orthocenter, Circumcenter, Congruence, Equilateral Triangle

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The figure shows a triangle ABC with orthocenter H and circumcenter O such that HB = OB. Line HO extended intersects AB and BC at D and E, respectively. Prove that triangle DBE is equilateral.
  

Geometry Problem 1147: Scalene Triangle, Orthocenter, Circumcenter, Congruence, Equilateral Triangle
 

See also:
Artwork of problem 1147
Kaleidoscope of Problem 1147 base on Poincare Disk Model.

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