Finding the Maximum Radius for a Chord.

Hey guys,

I want to find the Minimum/Maximum Radius for the following equation:

Area of a circle segment - Math Open Reference (Central angle in radians)

That is, assuming that Theta = 180 degrees. I think that's all the information I need to work it out, but I'm puzzled as how to figure out the final answer. It's a tiny part of a larger equation and I think my head is about to implode from the amount of times I've had to rethink how I approach the question. x.x

The question was taken from: http://nrich.maths.org/public/viewer.php?obj_id=5673

I'm not even sure whether I'm approaching this right.