In the context of circles, the radius is defined as:

The radius of a circle is correctly defined as half of the diameter. The diameter is the longest distance across the circle, passing through the center and touching two points on the circumference. Since the radius is the distance from the center of the circle to any point on its boundary, it is naturally half of this full distance represented by the diameter. Understanding this relationship is fundamental in both geometry and any discussions concerning circles, as it allows for easier calculations of areas and circumferences, which often utilize the radius and diameter interchangeably.

The other definitions provided do not accurately describe the radius: half of the circumference would not yield any relevant measurement for the radius; the diameter times π refers to the circumference; and the entire length around the circle describes the circumference itself, not the radius.