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Problem 31. Right
Triangle, Incenter. Level: High School, SAT
Prep, College geometry 
In
triangle ABC,
angle B is a right angle, E is the
incenter,
r is the
inradius,
EF is perpendicular to AE, FG is perpendicular to BC, ED is perpendicular to
CE, and DH is perpendicular to AB.
Prove that H, E, and G are collinear.
Hints: See
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