# Properties of a Circle Cheat Sheet - Concise & Comprehensive

# Properties of a Circle Cheat Sheet - Concise & Comprehensive

An overview of all the main properties of a circle including worked examples, labelled diagrams & more…

- Parts of a Circle
- Circumference of a circle
- Chords and Arcs
- Segments
- Tangents
- Diameter and Radius
- More on Arcs and Segments
- Sectors

## Parts of a Circle

## Circumference of a circle

The * circumference* of a circle is just the

*of it. So that is the length around the outside of the circle.*

**perimeter**To find the * circumference* of a circle we use the formula:

$Circumference = \pi \times diameter$

Or (it can also be written as)

$Circumference = 2 \times \pi \times radius$

## Chords and Arcs

A * chord* is a straight line that is drawn from any point around the edge of a circle to any other point around the edge of a circle.

An * arc* is a part of the circumference (around the outside of the circle). It’s just part of the edge sort of like a crust of a pizza slice.

## Segments

A * segment* is a section of a circle encloses by just a

*and an*

**chord***. So just draw a chord on a circle and you will have yourself two segments.*

**arc**## Tangents

A * tangent* of a circle is a straight line that just touches the edge of a circle at one singular point.

## Diameter and Radius

The * diameter* of a circle is the length from any point on the side of a circle to the other side of the circle, passing the centre point.

The * radius* is half of the

*so: The radius of a circle is the length from the centre of a circle to any point around the edge of the circle.*

**diameter**## More on Arcs and Segments

Like we mentioned earlier if you draw on a * chord* to a circle it will create 2

*.*

**segments**Naturally one will be larger than the other because if they were the same size, the chord would the the diameter and the two segments would be semicircles.

The larger segment is called the

major segmentand the smaller segment is called theminor segment.

Similarly, the circumference also divides into two sections or

arcsa smaller and larger arc - theminor arcand themajor arc.

## Sectors

A * sector* of a circle is just a section of the area of a circle. So it is enclosed by 2

*and an*

**radii***. It’s sort of like a slice of pizza but the point must be the exact centre of the circle - or pizza.*

**arc**As you have probably already worked out, if there is one * sector* the rest of the circle left over must also be a

*as well since it also is enclosed by the same 2*

**sector***and an*

**radii***.*

**arc**If you remember form earlier the larger arc is called the * major arc* and the smaller arc is the

*so you can guess what the different sectors are called… the*

**minor arc***and*

**major sector***.*

**minor sector**