Is there a consistent way to calculate the outer interval $\left(~\mbox{element of}\ \left[0, 2\pi\right]~\right)$ of a circle created by an intersection ?.
I calculated the intersection points and the angels with ${\rm atan2}$, but beyond that I'm clueless.
The radii of the circles and the positions of the centers are given. The blue circle would be at the center $\left(0,0\right)$.
For example, in this image I need the green interval:
The measure of the red arc is $$\alpha=2\arccos\left(\frac{d^2+r_2^2-r_1^2}{2r_2d}\right)$$ where $r_1$ is the radius of the blue circle and $d$ is the distance between the centers.
Note: $\arccos$ is usually written acos in programming languages.