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Problem 562: Triangle, Cevian, Incenter, Incircle, Perpendicular, Concyclic points, Cyclic Quadrilateral. Level: Math Education, High School, SAT Prep, College

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 points D, E, and G are concyclic (lie on a same circle).
 

Math Education: Triangle, Cevian, Incircle, Concyclic points
 

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