Go Geometry Problem Problem 328. Triangle, Incircle, Tangency Points, Parallel, Midpoint

The figure shows a triangle ABC with the incircle I and the tangency points D, E, and F. The line through A parallel to FE meets DE at G. The line through A parallel to DE meets FE at H. Prove that the line GH bisects AB and AC.
 

Triangle, incircle, parallel, midpoints
 

 

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