Definition
Circle
A circle is the closed curve made of all points in a plane that are the same distance from its centre.
What it means
Hold one end of a string at a fixed point and keep the string tight with a pencil at the other end. As the pencil moves all the way around, it traces a circle because its distance from the centre never changes.
Remember it
Same centre, same distance, all the way around.
Example
Mark centre C and choose a radius of 4 cm. Every point exactly 4 cm from C is on the circle. A point 3 cm from C is inside the circle, not on it.
Watch for
In precise geometry, the circle is its boundary. The filled region inside that boundary is a disk.
Common mix-up
Having no corners is not enough. An oval has no corners, but its points are not all equally far from one centre.
Exact meaning
A circle is the set of all points in a plane that are the same distance from one fixed point, called the centre. That fixed distance is the radius.