Online Geometry
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.