Geometry Problem 52: Triangle, Angle Congruence, Incircle, Angle Bisectors, Tangency Points

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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.
 

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