Problem 386. Triangle, Angle bisector, Perpendicular, Parallel,
Semiperimeter. 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. If FG is perpendicular to BC, prove that

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