# Area of Overlapping Circles

#### Mazaag

Joined Oct 23, 2004
255
Hey guys.

I need help guys. I know its simple but I have no clue how its done.

I have two circles, with the same radius, R, and I offset one by a distance X from the origin ( take the center of one of the circles as the origin). I need to calculate the area of the overlapping region. Since the two have the same radii, I assume that it shouldn't be thta complicated, but i'm completely STUCK and can't think ! :S

Thanks guys,

#### Papabravo

Joined Feb 24, 2006
18,980
Originally posted by Mazaag@Mar 15 2006, 03:26 PM
Hey guys.

I need help guys. I know its simple but I have no clue how its done.

I have two circles, with the same radius, R, and I offset one by a distance X from the origin ( take the center of one of the circles as the origin). I need to calculate the area of the overlapping region. Since the two have the same radii, I assume that it shouldn't be thta complicated, but i'm completely STUCK and can't think ! :S
Thanks guys,
[post=15033]Quoted post[/post]​
The answer from the following URL is:
Area of a chord

Rich (BB code):
Aoverlap = 2 * (R^2)* arctan[√ (((R/ (0.5*x) )^2) -1)] - x*( √ [R^2 - (x/2)^2] )

for x = 0, Aoverlap = pi*R^2 as we expect

and for x = 2R, Aoverlap = 0