>>11828140The equation for the angle x between the radii of the circular segment taking up the fraction F of the area of the circle is simply
x-sin(x) = 2piF
But the equation for the angle x between the radii of the intersection of two circular segments is
cos(z/2) cos(x-y/2) csc(x-y/2-z/2) (1-cos(y/2) sec(x-y/2))^2-sin(x) cos(y/2) sec(x-y/2)+x = 2piF
Where y and z are the radii angles of the intersecting segments.