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).