Problem 561: Triangle, Cevian, Incenter, Perpendicular,
90 Degrees.
Level: High School, College, Math Education The figure shows a triangle ABC with a cevian BD. Points E, F, and O
are the incenters of triangles ABD, BCD, and ABC, respectively. If
OG is perpendicular to AC, prove that the measure of angle EGF is 90
degrees.

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