Aha! Simen has found a solution to this part of the problem.

Concider the two circles, whose radi are1 and centres c1 and c2.

Now, translate and rotate the system so that c1 lies at <0, 0> and c2 lies
on <x, 0>, simply by letting c1' = 0 and c2' = c2 - c1, and rotating
with -theta, where tan theta = c2'.y/c2'.x.

Now, there are two points of intersection if the circles overlap (or one if
they are just "kissing".) By simple geometric judgement and using the
Pythagorean Theorem, we obtein the two intersections:

<x/2, sqrt(1-x^2/4)> and <x/2, sqrt(1-x^2/4)>

Now, rotate these points with +theta, and add c1, and you have the points of
intersection between the two circles.

5k.

>
>Yes, I too have found that that's the only way.
>Now I just need to know how to calculate all the
>points of intersection. How do I do that?
>

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