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Problem 387. Triangle, Angle bisector, Perpendicular, Concyclic points.
Level: High School, SAT Prep, College geometry.

The figure shows a triangle ABC with angle bisectors AD and CE of angles A and C, respectively. BD is perpendicular to AD and BE is perpendicular to CE. F is the intersection point of AD and CE, FG is perpendicular to BC, and FH is perpendicular to AB. Prove that points B,G,D,F,E, and H are concyclic. 

Triangle, Angle bisector, Perpendicular, Concyclic points 
 

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