If you remember how Venn Diagrams looked with the three intersecting circles, that is the context for this puzzle.

There are three circles, circle A, circle B, and circle C. Each circle passes through the center of the other two. What is the area of the intersection of these three circles?

Each circle will pass through the center of the other two, when the three radii are equal.
The area between an arc (formed by the itersection of a line and a circle) and intersecting line is = .5*r²(theta - sin(theta))
the area of the equilateral triangle with side r is = .5*r²*sin(π/3) = √3r²/4

So, area of intersection is = (3/2)r²((π/3) - (√3/2) ) + (√3/4)r²
= (π-√3)r²/2
= 0.704770923r²

Posted by Fahim on 2003-05-06 06:54:05