What is a radius?

A radius is defined as a line segment that extends from the center of a circle to any point on the circle's circumference. By this definition, the radius encompasses all the lengths from the circle's center to various points along its edge. This characteristic is crucial in understanding circle properties, as the radius remains constant for a given circle, which helps in calculating other measurements related to the circle, such as its area and circumference.

The other definitions do not align with the precise definition of a radius. A line segment that connects two points on the circle refers to a chord, not a radius. A line that passes through the center and extends to the circumference describes a diameter, which is effectively double the length of the radius. Meanwhile, a line that is parallel to the tangent of the circle does not relate to defining any segment that includes the center or the actual points on the circumference, making it irrelevant to the concept of a radius.