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

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

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

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 segment and the smaller segment is called the minor segment.

Similarly, the circumference also divides into two sections or arcs a smaller and larger arc - the minor arc and the major arc.

Sectors#

A sector of a circle is just a section of the area of a circle. So it is enclosed by 2 radii and an arc. It’s sort of like a slice of pizza but the point must be the exact centre of the circle - or pizza.

As you have probably already worked out, if there is one sector the rest of the circle left over must also be a sector as well since it also is enclosed by the same 2 radii and an arc.

If you remember form earlier the larger arc is called the major arc and the smaller arc is the minor arc so you can guess what the different sectors are called… the major sector and minor sector.