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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.

Triangle, Cevian, Incenter, Tangency point

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