Black holes, Intersection area

Hello. I've spent hours searching google for a formula to calculate the intersection area of two overlapping circles. The ones I've found only seem to work when they don't overlap too much. The black holes task itself doesn't seem too difficult and seemed like a fun problem(thanks for making it), but without being able to calculate the intersection area, I can't do it. So I have to give up now(spending lots of time searching google for a math formula isn't helping me learn to code).