Let C and D be circles in R2 which intersect in exactly two points. Prove that iD ◦ iC has exactly two fixed points in R2 ∪ {∞}.

Question

Let C and D be circles in R2 which intersect in exactly two points. Prove that iD ◦ iC has exactly two fixed points in R2 ∪ {∞}.

I do not understand how the composition of these two become fixed points? iD(p) and iD(p) would meet (if both through the point p).. But how do you find it generally through no point given?