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The crescent area created by overlapping circles

  1. Jan 9, 2007 #1
    Dear All,

    I need to know the area of the crescent created by overlapping circles;e.g. a circle radius 50µm overlapped by an equal circle with its centre 10µm to the left.
    Any help you can offer would be gratefully received,

  2. jcsd
  3. Jan 9, 2007 #2


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    Homework Helper

    Two steps:

    1. Consider a circle with center O, and a chord AB (ie, a line segment between two points on the circle). Find the area bounded by the arc AB and the line AB, ie, the area inside the circle and on one side of the chord. This can be done by finding the area of the pie slic corresponding to the arc AB and subtracting the area of the triangle ABO.

    2. Given two circles, the two points where they intersect form a chord on both circles, and sum of the two corresponding areas from 1 gives the area of overlap.
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