(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