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XiMS
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Points contained in a disk

I have a question, but not sure how to prove this.

We are given $n$ points in the Euclidean plane such that there exists no disk of radius $a$ which contains all of the points.

Conjecture: There must exist three of these points which are not contained in a disk of disk $a$.

Any idea about how to prove this?

Thanks.

XiMS
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