

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).







