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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
BG = DE. 

Triangle, Angle bisectors, Perpendicular, Congruence

 

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