Problem 320: Triangle, Circumcircle, Incenter, Excenter, Collinear points.
Level: High School, College, SAT Prep.
The figure shows a triangle ABC
with circumcircle C_{1}, incenter I, and excenter E
relative to BC. IE
intersect BC at F; IE intersect C_{1} at G. H is the
midpoint of arc AG. HI intersect C_{1} at M and HE
intersect C_{1} at N. Proved that M,
F, and N are collinear.

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