# Area of overlap of two circles.

• Nov 27th 2011, 02:55 AM
leart369
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
http://img827.imageshack.us/img827/3985/40412033.png
• Nov 27th 2011, 04:13 AM
agentmulder
Re: Looking for a solution of this problem
Quote:

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
http://img827.imageshack.us/img827/3985/40412033.png

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...
• Nov 27th 2011, 04:20 AM
Plato
Re: Looking for a solution of this problem
Quote:

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
http://img827.imageshack.us/img827/3985/40412033.png

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\$.