Checking and securing understanding of the parts of a circle | Maths

Starter quiz

What is the dashed line segment on this circle called?

arc

chord

circumference

diameter

radius ✓
The length of the diameter of this circle is ______ cm.

'13' ✓
The diameter of a circular fence is greater than 8 metres long. Which of these are possible lengths of the radius of this fence?

1 metre

π metres

4 metres

5.5 metres ✓

7 metres ✓
A semicircular sector has been cut from a full circle of equal radius. What fraction of the full circle is this sector?

$1\over2$ ✓

$2\over4$ ✓

$9\over10$

$180\over360$ ✓

$75\over100$
$This sector has been cut from a circle. What fraction of the full circle is this sector?$

This sector has been cut from a circle. What fraction of the full circle is this sector?

$1\over4$

$1\over5$ ✓

$1\over6$

$72\over100$

$72\over360$ ✓
This circular sector is broken down into two straight line segments and an arc. The perimeter of this arc is ______ cm.

'28' ✓

Exit quiz

What is the dashed line segment on this circle called?

arc

chord ✓

sector

segment

tangent
What is the shaded region on this circle called?

arc

sector

segment ✓

semicircle

tangent
Which of these statements are always correct?

A circular sector is made from exactly one radius on the circle and an arc.

A circular sector is made from exactly two radii on the circle and an arc. ✓

A circular sector is made from exactly one chord on the circle and an arc.

A circular sector is made from exactly two chords on the circle.

A circular sector is made from either radii or chords on the circle and an arc.
The size of the angle subtended by chord AB is ______ degrees.

'65' ✓
The size of the angle subtended by chord AC is ______ degrees.

'70' ✓
∠XOY is a 60° angle at the centre of a circle subtended by the arc XY. The circle has a radius of 42 cm. The area of the sector OXY is ______ cm² (2 s.f.)

'920' ✓

Worksheet

Loading worksheet ...

Presentation

Loading presentation ...

Video

Lesson Details

Key learning points

A chord splits the circle into two uneven pieces
The smaller piece is the minor segment and the larger is the major segment
Using fractions, you can calculate the area of a sector of a circle and you can calculate the curved length of a sector
To find the perimeter, you will need to add the radius twice
An exact answer may be given in terms of π

Common misconception

Pupils may think that every line segment that touches a circle exactly once is a tangent (even when it is not perpendicular to the radius at that point).

If unsure, try extending the line segment to beyond the edges of the circle to check whether it would intersect the circle again.

Keywords

Subtended - An angle can be subtended by a line segment or curve. The legs of the subtended angle meet the endpoints of the line segment or curve.