Thread: Problem 49
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Old October 30th, 2008, 05:58 AM
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CaptainBlack CaptainBlack is offline
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Originally Posted by CaptainBlack View Post
(minor variant of a problem due to Roy Barbara)

Let a,\ b,\ c be three positive real numbers.

Find necessary and sufficient conditions on a,\ b,\ c for there to exist an interior point P in the equilateral triangle ABC with unit side, such that |PA|=a,\ |PB|=b,\ |PC|=c.

I have a solution to this, but as I have not looked it up so I cannot tell if it is the originator's solution but as it is not as neat as I would like it is probably clumsy compared to the best solution, so lets see what we can do

CB
Ahh.. maybe its my modification to the question that is the reason my solution is clumsier than I would like??

I shall have to look into this possibility

CB
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