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Crescent

Definition

Defining inequalities

x^2 + y^2<=R^2 and (x - d)^2 + y^2>=r^2

Alternate name

Lamina properties

R>0 and r>0 and (d + r - R) (d - r + R) (-d + r + R)>0

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A = r^2 cos^(-1)((-d^2 - r^2 + R^2)/(2 d r)) - R^2 cos^(-1)((d^2 - r^2 + R^2)/(2 d R)) + 1/2 sqrt((d + r - R) (d - r + R) (-d + r + R) (d + r + R))

Distance properties

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p = 2 r cos^(-1)((d^2 + r^2 - R^2)/(2 d r)) + 2 R (π - cos^(-1)((d^2 - r^2 + R^2)/(2 d R)))

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