21.1 Parts of a circle — Learn

Prerequisites: name a point, line segment, angle and perpendicular lines.

Objectives: identify and use circle definitions and properties: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment.

Name the parts

The centre is the fixed point equally distant from every point on the circumference, the boundary of the circle. A radius joins the centre to the circumference. A diameter is a straight line through the centre joining two points on the circumference. It is twice the radius.

A chord joins two points on the circumference. A diameter is the longest chord. An arc is part of the circumference. A sector is the region between two radii and an arc. A segment is the region between a chord and its arc. A tangent is a straight line that touches a circle at one point.

Example 1. A circle has radius $4.6$ cm. Work out its diameter.

The diameter is two radii: $d=2r$.

Substitute $r=4.6$: $d=2(4.6)$.

Calculate: $d=9.2$ cm.

Example 2. A chord is $7$ cm long. Can it be a diameter of a circle with radius $3$ cm?

The diameter is $2(3)=6$ cm.

A chord cannot be longer than the diameter, and $7>6$.

So the chord cannot belong to this circle.

Watch out. A radius is not the whole distance across a circle. Check: the diameter is two equal radii, so $d=2r$.

Check your circle vocabulary

A line joins two points on a circle and passes through its centre. Name the line, then explain how it is related to a chord.

You should now be able to

• identify and label the centre, radius, chord and diameter;
• identify the circumference, tangent, arc, sector and segment;
• use the facts that a diameter is twice a radius and is the longest chord.