Basic geometry question regarding hexagons.

[Gazarai]

I'm trying to figure out how to find the longest diameter of any irregular hexagon with 3 different sets of sides. Each side is the same in length as the side opposite it, and different in length to both sides beside it. Any help?

 

[Gazarai]

Err, I should note that I know *how* to find it, and that what I can't seem to figure out is how to put it into a formula, with 3 variables representing the 3 sets of sides.

 

[adriank]

Is the largest possible diameter not half the perimeter, using a degenerate hexagon?

Or is there something you haven't told us, say, regarding the angles?