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.

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 radius $a$.

Any idea about how to prove this?

Thanks.

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 circle of disk $a$.

Any idea about how to prove this?

Thanks.

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.

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 circle of radius $a$ which contains all of the points.

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

Any idea about how to prove this?

Thanks.

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 circle of disk $a$.

Any idea about how to prove this?

Thanks.