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 end up being the center of our circle like the red dot in diagram 1 below:
Diagram 1
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).
Diagram 2
Now,, we just have to make so many dots that they connect toghether to become a true circle as shown in the animation below.
Animation
The distance of '5' is known as the radius.
