The radius of a circle is a very important part of the circle.
First, let's define what a circle is.
A circle is defined as a set of points in a plane that are a given distance from a given point in the plane.
At first, that may be confusing but let's break it down.
The given point is called the center of the circle or sometimes referred to as the origin and the given distance from any point on the circle to the center is called the radius of the circle.
Whichever point on the circle we choose, the distance to the center of the circle will always be the same so we can say that all radii of a given circle are congruent.
So, the radius is important because it's the distance from the center of a circle to any other point on the perimeter of that circle.