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Parallelograms (Posted on 2017-09-09) Difficulty: 4 of 5

  
Let ABC be an acute triangle with altitudes AD and BE. The
intersection of AD and BE is H. Points F and G make CADF
and CBEG into parallelograms. M is the midpoint of FG.
Ray MC intersects the circumcircle of ΔABC again at point N.

Prove that ANBH is a parallelogram.
  

See The Solution Submitted by Bractals    
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May I have a hint, please? | Comment 1 of 5
There's a lot going on in this problem, but I feel the key may be to add a line or two.  Where?  It's easy to prove angles ANB and BNA are equal but that's all I've got.
  Posted by Jer on 2017-09-11 20:52:59
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