Thread: Problem 49
View Single Post
  #4  
Old November 22nd, 2008, 01:24 AM
David24 David24 is offline
Banned
  
Join Date: Nov 2008
Posts: 82
Country:
Thanks: 0
Thanked 25 Times in 25 Posts
David24 is on a distinguished road
Default
Quote:
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

Is the solution to this problem not simply a = b = c??

Cheers,

David