geometry

Two circles of equal radius intersect each other such that each circle passes through the center of the other circle. Find the equation for the perimeter of this figure.

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  1. We assume the y-axis to be the common chord, i.e. the centres of the circles are at (-r/2,0) and (r/2,0).

    The two circles will therefore respectively be:
    (x+r/2)²+y²=r² (x≤0)
    and
    (x-r/2)²+y²=r² (x≥0)

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  2. The equation for the perimeter of the two intersecting circles of radius R is
    P = 2(Pi)R(2)240/360 = 8PiR/3.

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