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Problem 385. 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. Prove that (1) DE is parallel to AC.
(2) If s is the semiperimeter of triangle ABC, DE = s - b.
 

Triangle, angle bisectors, perpendiculars, parallel
 

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