# Formulary:Maths - Geometry - Circle ○

## Circle ○

A circle is a basic shape consisting of the points at a given distance from a given point on a plane.

### Definitions:

• r: Radius
• d: Diameter
• U: Circumference
• A: Area

#### Circumference of a Circle

The circumference U is the distance around a closed curve.

$${\color{blue} {U}} = 2 \times \pi \times {\color{red} {r} }$$
U = Circumference
r = Radius

$${\color{red} {r}} = \frac{ {\color{blue} {U} } }{ 2 \times \pi }$$
r = Radius
U = Circumference

$${\color{blue} {U}} = \pi \times {\color{red} {d} }$$
U = Circumference
d = Diameter

$${\color{red} {d}} = \frac{ {\color{blue} {U} } }{ \pi }$$
d = Diameter
U = Circumference

#### Area of a Circle

The region inside a circle.

$${\color{OliveGreen} {A}} = \pi \times {\color{red} {r} }^{2}$$
A = Area
r = Radius

$${\color{red} {r}} = \sqrt{ \frac{\color{OliveGreen} {A}}{\pi} }$$
r = Radius
A = Area

$${\color{OliveGreen} {A}} = \frac{\pi}{4} \times {\color{red} {d} }^{2}$$
A = Area
d = Diameter

$${\color{red} {d}} = \sqrt{ \frac{4 \times {\color{OliveGreen} {A} } }{\pi}}$$
d = Diameter
A = Area