Two circles of radius 1 intersect in such a way that the perimeter of each circle passes through the center of the other circle. Show that the area of intersection (the GREEN area) has area: 2*pi/3 - sqrt(3)/2.
- Draw an equilateral triangle with vertices at the centers of the circles and at the point of intersection of the two circles at the top of the figure
- Calculate the area of the triangle: 1/2 * base * height = 1/2 * sqrt(3)/2
- Area of corresponding sector of the circle = pi/6
- Difference between areas = pi/6 - sqrt(3)/4
- Add this difference to the area of the sector of the circle. The result is: pi/3 - sqrt(3)/4
- Multiply by 2 to include the lower half of the green area
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