Inductive proof problem

Good Anonymouses, this anonymous is having a little trouble with starting this induction proof:

Two non-overlaping circles of radius 1 intersect in exactly two points. Prove by induction that given n >= 2 non-overlapping circles in the plane that the total number of intersections is never more than n(n-1).

I know this is true and I can see why, but I don't know what to do after I've done the base case and the inductive hypothesis.

>>4
How would one add that to the proof? Wouldn't I need to prove that adding a circle to n circles will at most add 2n intersections first before I can use it?

This is actually the problem I'm having, its the word problems. If it was a simple "2^n < n!" or something I can do it but when it comes to word problems I don't know how to formula a sort of equation that would let me prove something.