Two pi or not two pi

Calculus Level 5

This closed curve satisfies the equation \[\sqrt{1-|x|} + \sqrt{1-|y|} = 1.\] It looks much like the unit circle but is a little bulgier. Not surprisingly, the circumference \(C\) of this curve is slightly greater than that of the unit circle.

By what percent is this circumference greater than that of the unit circle? In other words, what is \[\frac{ C - 2\pi}{2\pi} \times 100?\]

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