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Geometry Problem 321: Triangle, Incenter, Excircle, Midpoint of the Altitude, Collinearity

The figure shows a triangle ABC with incenter I, and M midpoint of the altitude AH. If F is the point of tangency of BC and the excircle relative to BC, prove that M, I, and F are collinear.
 
 
 

a

 

See also: Typography of problem 321

 


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