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.

Answer 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)

Answer 2

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