(minor variant of a problem due to Roy Barbara)

Let be three positive real numbers.

Find necessary and sufficient conditions on for there to exist an interior point in the equilateral triangle with unit side, such that .

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