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Problem 476: Triangle, Circumcenter, Circumcircle, Angles

The figure shows a triangle ABC. D is a point on CA extended, F a point on CB extended, and E a point on AB. If points, G, H, and M are the circumcenters of triangles CDF, ADE, and BEF, respectively, prove that angles BAC and MHG are congruent.

Triangle. Circumcenter, Angles