Write a function to compute the area of the shaded moon-shaped region in the figure below—that is, the area of a smaller circle that does not overlap with a larger circle. The input will be the radius a of the smaller circle, the radius b of the larger circle, and the separation c between centers of the circles.
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When c is close to b-a (as in test case 4, with a=3, b=4, c=1.01) the solutions are susceptible to roundoff error; after some checking, I believe the correct answer for test case 4 (to 15 significant figures) should be A=0.00650196332827386 rather than A=0.006501963328256.
I changed the tolerance on that test.