# Thread: Area of overlap of two circles.

1. ## Area of overlap of two circles.

Can someone tell me how to find the grey area in the drawing knowing the radius of both circles,wich has on both circles the same value

2. ## Re: Looking for a solution of this problem

Originally Posted by leart369
Can someone tell me how to find the grey area in the drawing knowing the radius of both circles,wich has on both circles the same value
Here is a way, construct the equilateral triangle inside the shaded area connecting the centers of the circles and one point of intersection. You now know the area of the sector, given by (r^2/2)ß, ß = pi/3 and you can find the area of the triangle using pythagorean theorem and (base*height)/2

continue...

3. ## Re: Looking for a solution of this problem

Originally Posted by leart369
Can someone tell me how to find the grey area in the drawing knowing the radius of both circles,wich has on both circles the same value
If you draw a line segment between the two points of intersection then two circular segments of equal area are formed.
Go to that webpage. Formula #17 gives the area.
But there is a problem: Their $\displaystyle R$ is your $\displaystyle r$.
There $\displaystyle r$ is your $\displaystyle \tfrac{1}{2}r$.