I'm trying to figure out how to calculate the points at which two circles intersect, identical to this, (I can't find any code for it) I'd like to know how to find the coordinates where the dots are drawn. 

I found a thread with a method that works, but I don't understand the math behind it. There was also  this, which I think Casey Reas' approach is based on. 

So I guess I'm looking for a math explanation, or any links to help me understand how to make an implementation. 

Thanks