A **circle** is a shape that is round.

It has infinite lines of symmetry through the centre of the circle.

## Contents

## Formulae[edit | edit source]

To find the area and circumference of a circle, use these formulae:

(for area)

(for circumference)

## Circle Theorems[edit | edit source]

A circle has many relationships between its angles.

### Angles Subtended on the Same Arc[edit | edit source]

Angles formed from two points on the circumference are equal to other angles, in the same arc, formed from those two points.

### Angle in a Semi-Circle[edit | edit source]

Angles formed by drawing lines from the ends of the diameter of a circle to its circumference form a right angle. So c is a right angle.

### Angle at centre[edit | edit source]

The angle formed at the centre of the circle by lines originating from two points on the circle's circumference is double the angle formed on the circumference of the circle by lines originating from the same points. i.e. a = 2b.

## Sector[edit | edit source]

The area of a sector =