geometry

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Circle A has radius 6. Circle B has radius 10. They cross at two points that are 5 apart. What is the overlapping area?

  • geometry -

    we want the area of a segment of each circle, subtended by a chord of length 5.

    A: α = 2 arcsin(2.5/6) = .860
    B: β = 2 arcsin(2.5/10) = .506

    area is thus

    1/2 6^2 (α-sinα) + 1/2 10^2 (β-sin)
    = 18(.860 - 5/6) + 50(.506 - 1/2)
    = 0.780

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