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Maximizing product (Posted on 2013-09-19) Difficulty: 3 of 5
In a triangle ABC two items are defined : the side AB=c and the height from point C to this side Hc= k.

What is the maximum value of the product Ha*Hb* Hc ?

No Solution Yet Submitted by Ady TZIDON    
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re: solution | Comment 2 of 4 |
(In reply to solution by Dan Rosen)

Looks right to me when k <= c/2, and I didn't manage to get this far.  Nice start!

When k > c/2, however, I think you will find that Gamma = 90 degrees cannot be attained.  In this case, I expect that Gamma (and the desired product) is maximized by an isosceles triangle with AB as its base.

Edited on September 23, 2013, 7:54 pm
  Posted by Steve Herman on 2013-09-23 09:19:51

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