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Problem 564: Complete Quadrilateral, Incenter, Excenter, Concyclic Points, Incircle, Excircle. Level: High School, SAT Prep, College

The figure shows a complete quadrilateral ABCDEF. G and N are the excenters of triangles ABE and ADF, respectively. H and M are the incenters of triangles BCF and CDE, respectively. Prove that the points G, H, M, and N are concyclic (lie on a same circle). 

Complete quadrilateral, Incenter, Excenter, Concyclic points
 

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