Deal with plane convex sets.A plane convex set, subsequently abbreviated to "convex...

Deal with plane convex sets.A plane convex set, subsequently abbreviated to "convex set," is a nonempty set X in the plane having the property that if x and y are any two points in X, the straight-line segment from x to y is also in X. The following figures illustrate.

Suppose that n ≥ 3 points in the plane have the property that each three of them are contained in a circle of radius 1. Prove that there is a circle of radius 1 that contains all of the points.