The locus of points idea allows you to define a circle without giving a numerical value for the radius.

Yes, the locus of points idea is a fundamental concept in geometry that allows us to define shapes based on their properties, rather than numerical measurements.

In the case of a circle, it can be defined as the locus of all points that are equidistant from a fixed point (the center). This definition does not require a specific numerical value for the radius. Instead, it simply states that all points on the circle are the same distance from the center, whatever that distance (or radius) may be.

Here are the steps to define a circle using the locus of points idea:

1. Choose a fixed point. This will be the center of the circle.
2. Choose a distance from the fixed point. This will be the radius of the circle. Note that we are not assigning a specific numerical value to the radius. We are simply stating that there is a certain distance that all points on the circle will be from the center.
3. The circle is then the set of all points that are this chosen distance from the fixed point.

So, the locus of points idea allows us to define a circle in a way that is independent of a specific numerical radius.