Problem 384. Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter. Level: High School, SAT Prep, College geometry.
The figure shows a triangle ABC with
external 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) DE is equal to the semiperimeter of triangle ABC.