In geometry, a locus (plural loci) is a set of points which satisfies a given condition or situation for a shape or a figure. The word locus is derived from the word location. Before the 20^th century, geometric shapes were considered as an entity or place where points can be located or can be moved. But in modern Mathematics the entities are considered as the set of points that satisfy the given condition. In this sub-topic, we will explore the circle as a locus.

The locus of points defines a shape in geometry.

A circle is the locus of all the points which are equidistant from the center. So, a circle as a locus can be defined as follows:

Definition

With respect to the locus of the points or loci, the circle is defined as the set of all points equidistant from a fixed point, where the fixed point is the center of the circle and the distance of the sets of points from the center is the radius of the circle. Let us say, O is the center of the circle and r is the radius of the circle, that is, the distance from point O to the set of all points or the locus of the points.

To be able to understand the properties of a circle and use them in different applications, you must be aware of the basic terms related to a circle.

Definition

(a) The distance from the center of a circle to any point on its boundary is called radius of circle.
(b) A line segment passing through the center that connects two points on the boundary is called diameter of circle.
(c) Any line segment touching the circle at two different points on its boundary is called chord of a circle.