How is the radius of a circle defined?

The radius of a circle is defined as a line segment that joins the center of the circle to any one point on the circle. This description captures the fundamental characteristic of the radius, which is a measure of distance from the center to the circumference. Since all points on the circle are defined as being equidistant from the center, any line segment drawn from the center to any specific point on the circle exemplifies this definition.

In contrast, other concepts provided in the choices relate to different properties of a circle. A line segment that passes through the center of the circle describes a diameter, which is specifically twice the length of the radius, rather than defining the radius itself. The total distance around the circle refers to the circumference, which is a separate measurement entirely. Lastly, a single point equidistant from every point on the circle describes the center of the circle, not the radius. Each of these other concepts is relevant to the study of circles but does not accurately capture what a radius is.