I have two circles with radii $r$ and $R$. I need to know how far apart to draw them so that their intersection has area $A$. Basically, I'm solving for $d$ in the diagram seen in the MathWorld link.
It's not hard to solve for $A$ (see MathWorld),
$A = r^2\cos^{-1}\left(\frac{d^2+r^2-R^2}{2dr}\right) + R^2\cos^{-1}\left(\frac{d^2+R^2-r^2}{2dR}\right)-\frac{1}{2}\sqrt{(-d+r+R)(d+r-R)(d-r+R)(d+r+R)}$
but I've been struggling to find a solution for $d$.