A small circle starts concentric with a large circle, but moves radially outward. At some point, part of the small circle extends beyond the large circle. How much of the small circle's circumference is outside, as a function of radial distance traveled by the small circle from the center of the large circle? Area?
Slope of this function is probably very large when it first exits, especially if the circles are similar in size.
GPS Dilution of Precision.
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