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Well, I can prove it's correct.

You only have to show that the optimal pair of circles is to be found among the set of minimal circles (*) (and not just any circles). And that's easy. Say you have...

I have an idea but it's O(N^6) so it's probably wrong :). I give it without proof and without much detail so you can mull it over yourself.

Using 3, 2 or 1 point(s) you can define a minimal...