What is the definition of the center of a circle?

The center of a circle is defined as a single point inside the circle that is equidistant from every point on the circle. This means that if you were to measure the distance from the center point to any point on the circumference of the circle, each of those distances would be the same. This property is fundamental to the definition of a circle itself, as it establishes the uniformity of the shape and helps in understanding various geometric concepts related to circles, such as radius, diameter, and circumference.

In contrast, other options describe different geometric concepts related to circles. A line segment that joins the center to any point on the circle refers to a radius, while a line segment that passes through the center typically describes a diameter. The total distance around the circle, known as the circumference, relates to the circle's perimeter, but does not define the center itself. This distinction is critical in grasping not only the definition of a circle but also the relationships between its parts.