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Problem 30. Right
Triangle, Incenter, Inradius. 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 and FG is perpendicular to BC.
Prove that BG = 2r.
Hints: See
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