++ This is one of those times I wish I could double ++ a post. I only beat you to the punch 'cause you actually *did* it. It was an interesting enough problem that I could've done it. But I wouldn't have an answer until tomorrow... ;^)

(Especially as I would've wasted my time on a recursive backtrack to "optimize" the circle, but your results show that it's unneeded.)

--Roboticus