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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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Hints/Tips re: May I have a hint, please? | Comment 3 of 5 |
(In reply to May I have a hint, please? by Jer)

When I made my first reply I missed:


"It's easy to prove angles ANB and BNA are equal..."

Unless you are using directed angles, ANB and BNA are always equal.

I'm still having a problem showing that the ray MC passes through the circumcenter of triangle ABC. 

If I could do that, then proving that ANBH is a parallelogram is easy.

If I could prove ANBH is a parallelogram, then proving that the 
ray MC passes through the circumcenter of triangle ABC is easy.

  Posted by Bractals on 2017-09-18 22:38:15
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