The locus of a moving point that maintains equidistant from a fixed point is called a circle.

Circle is a plane round shape figure and it is one of the most significant geometrical shapes in geometry. It is actually formed in two different ways.

A point which moves around another point with equidistant.

Joining the points which are located at equal distance from a point.

These two methods form round shape figure geometrically and it is called as circle. Here, you understand how exactly a circle is formed in geometric system.

Construction

Consider a point in the plane and it is called as point $O$.

Consider another point in the plane and assume to call it as point $P$ and it is located at $r$ units’ distance from the point $O$.

Identify the points which are located at equal distance ($r$ units) from the point $O$. Therefore, the distance from point $O$ to point $P$ is exactly equal to distance from point $O$ to each surrounded point displayed in the below figure.

Now, join all the points and it forms a round shape figure, called circle.

Instead, assume the point $P$ is moved in round shape by maintaining equal distance from the point $O$. The point $P$ is known as variable point because it represents all the points which are located at same distance from point $O$. The locus of the moving point gives a round plane figure and it is known as circle. The locus of variable point can be understood in this video tutorial.