### Formal Definition

A circle is a locus of points that are all equidistant from another point, called the center.

#### So, what the heck does that mean?

That formal definition means that if you take some point which will be the center of our circle like the red dot in diagram 1 below:

And then make a whole bunch of other points exactly 5 units away (see diagram 2), then all of those points are equidstant from the red dot. These big outer dots are the start of a circle. They are a locus of points 5 units from the center (ie they are a bunch of points that are 5 units from the red dot ).

Now,, we just have to make so many dots that they connect toghether to become a true circle as shown in the animation below The distance of '5' is known as the radius.

And then make a whole bunch of other points exactly 5 units away (see diagram 2), then all of those points are equidstant from the red dot. These big outer dots are the start of a circle. They are a locus of points 5 units from the center (ie they are a bunch of points that are 5 units from the red dot ).

Now,, we just have to make so many dots that they connect toghether to become a true circle as shown in the animation below The distance of '5' is known as the radius.