When examining the concept of a radius within the context of a circle, it is defined as a line segment that extends from the center of the circle to any point on the perimeter of the circle. This definition inherently indicates that the radius spans from the very center of the circle outward, connecting directly to the circle's edge.
Given this understanding, the statement "A radius is a segment that connects any point on the circle to the center of that circle" aligns precisely with the mathematical definition of a radius.
Thus, the correct answer is:
A. True
