Problem 52.
Triangle, angles, incircle.
Level: High School, SAT Prep, College

In the figure below, a
circle of
center O
inscribed
in a
triangle ABC is
tangent to sides BC, AC, and AB at
points
D, E, and F, respectively.
Lines
AO and FD meet at H, and lines CO and DF meet at G.
Prove
that angle GEH is congruent to angle ABC.