Infographic Geometry Problem 1060: Triangle, Incircle, Incenter, Inscribed circle, Tangent, Angle. Level: High School, SAT Prep, College, Mathematics Education

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In a triangle ABC (see the figure below), the incircle of center I is tangent to BC, AC, and AB at D, E, and F, respectively. BI extended meets DE at G. Prove that angle C = 2 angle IFG.

$Infographic Geometry problem: Triangle, Incircle, Incenter, Inscribed circle, Tangent, Angle$