A circle is a shape formed by a curve such that all points on the curve are the same distance from a fixed point, called the centre.



The circumference is the distance around a circle.

radius is the distance from the centre to any point on the circumference.

diameter is a chord that passes through the centre.
The length of the diameter is twice the length of the radius.

An arc is a part of the circumference.

chord is a straight line joining two points on the circumference.

segment is an area of a circle bounded by a chord and the circumference.

A sector is an area of a circle bounded by two radii and the circumference.

tangent is a line that touches the circumference of a circle at only one point.


pi.jpgπ (Pi)


π is a fixed number (called a constant). It is the ratio of the length of the circumference to the length of the diameter.

Y9_Circles_02.gif This ratio is the same for ALL circles. 

π is an irrational number and cannot be calculated exactly but is equal to 3.141592 (to 7 significant figures)

A good fractional approximation to π is 227.



The perimeter of a circle is called the circumference

C = 2π r

= π d



Area of Circle

A = π r2

Examples of Circle Calculations

Example 1

Find the circumference and area of a circle of radius 6 cm.

Use π = 3.1

C = 2π r

C = 2 × 3.1 × 6

C = 37.2 cm


A = π r2

A = 3.1 × 6 × 6

A = 111.6 cm2

Example 2

Find the area of the sector shown below if the radius of the circle is 8 cm.


Use π = 3.1


Angle of sector = 90°

Fraction of circle = 90⁄360 = 1⁄4

Area of sector = 0.25 × Area of circle

= 0.25 × πr2
= 0.25 × 3.1 × 82
= 49.6 cm2
Example 3

Find the radius of a circle that has a circumference of 55.8 cm.

(Use π = 3.1)

C = 2πr

55.8 = 2 × 3.1 × r

6.2r = 55.8

r = 55.8⁄6.2

r = 9 cm