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By the definition of a sphere, there is one point inside it such that the distance between that point and any given point on the surface of the sphere are equal, and that point is called the center of the sphere.

The diameter of a sphere is the length of any straight line drawn from a point on the surface to another point on the surface through the center.

In the words of Euclid:

A diameter of the sphere is any straight line drawn through the centre and terminated in both directions by the surface of the sphere.

(The Elements: Book $\text{XI}$: Definition $17$)