My algebra is letting me down here, I can't figure out how to arrange this equation - anyone prepared to give me a hand?
The area of the intersection of two circles can be defined as $$A = r^2 \cos^{-1}\left(\frac{d}{r}\right) - d \sqrt{r^2 - d^2} + R^2 \cos^{-1}\left(\frac{d}{R}\right) - d \sqrt{R^2 - d^2}$$ Where:
- $r$ is the radius of circle one
- $R$ is the radius of circle two
- $A$ is the area of their intersection
- $d$ is the distance between the two circles' centres.
But, if I have numerical values for all of these variables except $d$, how can I reform the equation to find it?
Don't try to do this analitically. You can find $d$ only by a numerical method (http://en.wikipedia.org/wiki/Root-finding_algorithm).