Two circles have the same radius 1 unit. If each circle passes through the centre of the other circle, what is the area common to the two circles?
Area of two circles is 2pi. But how could I find the common area?
So area of two equilateral triangles is $\displaystyle \frac {\sqrt 3}{2}.$
Area of 4 segment = $\displaystyle 4 \times \frac{1}{2} (\frac {\pi}{3} - \frac{\sqrt 3}{2}) = \frac {2}{3} \pi - \sqrt 3 $
Therefore, enclosed area = $\displaystyle \frac {\sqrt 3}{2} + \frac {2}{3} \pi - \sqrt 3 = \frac {2}{3} \pi -\frac {\sqrt 3}{2}$
Is this right?