I would like to know if is possible calculate the area between 2 rings with opposite centers and the same radius, that is:  $$r_1^2&lt;(x-a)^2+(y-b)^2&lt;r_2^2$$ $$r_1^2&lt;(x+a)^2+(y+b)^2&lt;r_2^2$$  I think that depend on the relation between center and radius, but I'm not sure.  I'm working on...  Edit:  This is an example   $$4&lt;(x-1){}^2+(y-2){}^2&lt;8$$  $$4&lt;(x+1){}^2+(y+2){}^2&lt;8$$
Given two separate annulus with centers $[C_1,C_2]$ and their corresponding radii being $[R_1,r_1]$ and $[R_2,r_2]$ respectively, larger radius being $R$. There are methods to look at whether they are overlapping or not. If they overlap how to find the overlapping area. Is there any close form expression for it?  equation of first annulus   $r_1^2&lt;(x-x_{c1})^2 + (y-y_{c1})^2 &lt;R_1^2$   equation of second annulus  $r_2^2&lt;(x-x_{c2})^2 + (y-y_{c2})^2 &lt;R_2^2$  If there are three circles overlapping, we get overlapping area as solution to set of 4 in-equations by least squares approach(Though we don't end up getting total area but, area within tangents of circles ).
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