List of intersections circles.

I have a list of circles, with different centers and radious. The are all in the same plane and I want to know which have a surface intesection. At the moment I don't even care about where they intersec (maybe in the future) Just need a list with the points which cicles have a surface in common.

At the end I will make an optimazation system that add new points inside the circles and which position is inside each circle, so the intersection surface means shared points (not all the posible intersection will be suitables so the list has to be complete). Every point has to be joined with one and only one new node, but it would be part of the combination system.

Thanks for your help, I am really new to grasshopper and still new to programing.