Geometry » Circles

What is a circle?

The definition of a circle is:
A set of points in a plane that are equidistant to a given point, the centre.
The blue line in the drawing below is the circle. So not the area within.

Circle with radius drawn in

The distance between the centre and the circle is called the radius*1.
The distance circle-circle through the centre is called the diameter.
The perimeter of the circle is called the circumference.

Calculating with circles

diameter = 2 × radius
radius = 12 × diameter (or diameter : 2)
area circle*2 = radius × radius × π
circumference = diameter × π

In letters and as short as possible:
d = 2r
r = 12d
A = πr2
C = dπ

*1 The plural form of radius is radii.
*2 With the area of the circle, we mean the area enclosed by the circle.
The area within the circle is actually called a disc.