What is G9: Circle definitions?

Use circle vocabulary precisely. A radius joins the centre to the circumference.

How many marks are G9 questions worth?

In verified past-paper appearances, G9 questions on Edexcel GCSE Maths 1MA1 have been worth 1–4 marks.

Which past exam papers has G9 appeared in?

G9 has appeared in 8 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

Identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment

Circle definitions

Worked answers, methods and verified real exam appearances for G9 on Edexcel GCSE Maths 1MA1.

Explanation

Use circle vocabulary precisely. A radius joins the centre to the circumference.
A diameter is a chord through the centre and has length $2r$ . A chord joins two points on the circumference, while a tangent meets the circle at exactly one point.
An arc is part of the circumference. A sector is bounded by two radii and an arc; a segment is bounded by a chord and an arc.
The minor region uses the shorter arc and the major region uses the longer arc.
In a labelled-diagram question, identify the defining boundaries rather than relying on a region's appearance.

Key circle parts: centre, radius, diameter, chord and tangent.

Worked example

A circle has diameter $18$ cm. A chord $AB$ does not pass through the centre. State the radius and name the two regions cut off by chord $AB$ .

1.Use $d=2r$ , so $r=18\div2=9$ cm.
2.A chord and each corresponding arc bound a segment.
3.The shorter-arc region is the minor segment and the longer-arc region is the major segment.

Answer: The radius is $9$ cm; chord $AB$ forms a minor segment and a major segment.

Common mistakes

Don't call any chord a diameter even though it does not pass through the centre.
Don't confuse a sector, bounded by two radii and an arc, with a segment, bounded by a chord and an arc.

Exam tip

For a circle-definition mark, name the boundary pieces explicitly: radii, chord or arc.

Worked practice

Tier 1 · Easy

A circle has radius

6.5

cm. Write down its diameter.

(1)

(Total for Question 1 is 1 mark)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	$13$ cm	1	The diameter is twice the radius, so $d=2\times6.5=13$ cm.

Tier 2 · Standard

A straight segment joins two points on a circle but does not pass through its centre. Another straight line meets the circle at exactly one point. Give the geometric name of each.

(2)

(Total for Question 2 is 2 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	The segment is a chord; the line is a tangent.	2	A segment whose endpoints lie on the circumference is a chord. A line meeting a circle at exactly one point is a tangent.

Tier 3 · Hard

A circle is centred at

O

. Distinct points

A

and

B

are on its circumference, and

AB

is not a diameter. Describe precisely the boundaries of the minor sector

AOB

and the minor segment cut off by

AB

(3)

(Total for Question 3 is 3 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	The minor sector is bounded by radii $OA$ and $OB$ and the minor arc $AB$ ; the minor segment is bounded by chord $AB$ and the minor arc $AB$ .	3	A sector uses two radii plus their connecting arc. A segment uses a chord plus its corresponding arc. Selecting the shorter arc $AB$ gives the minor sector and minor segment.

Tier 1 · Easy

Write down the name of the part of a circumference between two points on a circle.

(1)

(Total for Question 4 is 1 mark)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	Arc	1	A part of the circumference between two points is called an arc.

Tier 2 · Standard

Draw a circle with centre

O

. Mark points

A

and

B

on the circumference, draw chord

AB

, and shade the minor segment cut off by

AB

(2)

(Total for Question 5 is 2 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	A correctly labelled circle with chord $AB$ drawn and the smaller region between chord $AB$ and the minor arc $AB$ shaded.	2	Draw the circle and label its centre $O$ . Put $A$ and $B$ on the circumference and join them with a straight chord. Shade the smaller region bounded by chord $AB$ and the minor arc $AB$ .

Tier 3 · Hard

Distinct points

A

and

B

lie on a circle. The shorter arc

AB

has length

14

cm and the circumference is

50

cm. Give the geometric name and length of the other arc from

A

B

. Work out what fraction of the circumference the shorter arc is. Give the fraction in its simplest form.

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	The major arc $AB$ , with length $36$ cm $\dfrac{7}{25}$	3	The other arc is the longer route around the circumference, so it is the major arc. Its length is $50-14=36$ cm. The shorter arc is $\dfrac{14}{50}$ of the circumference; dividing the numerator and denominator by $2$ gives $\dfrac{7}{25}$ .

Tier 2 · Standard

Points

P

and

Q

lie on a circle and are not endpoints of a diameter. Write down the geometric name of the longer route from

P

Q

along the circumference, the straight segment

PQ

, and the larger region between this route and

PQ

(3)

(Total for Question 7 is 3 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	Major arc $PQ$ ; chord $PQ$ ; major segment	3	The longer part of the circumference is the major arc $PQ$ . A straight segment joining two points on the circumference is a chord. The larger region bounded by that chord and the major arc is the major segment.

Tier 3 · Hard

A circle has centre

O

, with

A

B

C

and

D

on its circumference. Segment

AB

passes through

O

, but segment

CD

does not. Explain why the statement 'every diameter is a chord, but not every chord is a diameter' is correct.

(3)

(Total for Question 8 is 3 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	$AB$ is both a diameter and a chord; $CD$ is a chord but not a diameter because it does not pass through $O$ .	3	Both endpoints of $AB$ are on the circumference, so it is a chord, and it passes through the centre, so it is also a diameter. Segment $CD$ also joins two points on the circumference, making it a chord, but it misses the centre and therefore is not a diameter.

Tier 3 · Hard

A circle with centre

O

has radius

7

cm. The perimeter of minor sector

AOB

31

cm. Chord

AB

is drawn. Work out the lengths of the minor and major arcs

AB

. Write down the names of the smaller and larger regions bounded by chord

AB

and the circumference.

(5)

(Total for Question 9 is 5 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	Minor arc $=17$ cm; major arc $=14\pi-17$ cm; minor segment and major segment	5	The perimeter of a sector is two radii plus its arc, so the minor arc has length $31-2\times7=17$ cm. The full circumference is $2\pi\times7=14\pi$ cm, hence the major arc has length $14\pi-17$ cm. A region bounded by a chord and an arc is a segment: the smaller one is the minor segment and the larger one is the major segment. Taking $O=(0,0)$ , $A=(7,0)$ and $B=(7\cos(17/7),7\sin(17/7))$ verifies the minor arc because $17/7<\pi$ ; its length fixes the central angle uniquely up to rotation or reflection.

Q10

Tier 3 · Hard

The circumference of a circle is

84

cm. Points

A

and

B

divide the circumference into two arcs whose lengths are in the ratio

2:5

. Chord

AB

is drawn. Work out both arc lengths, name the smaller region between

AB

and the circumference, and name the larger region bounded by

OA

OB

and the circumference.

(4)

(Total for Question 10 is 4 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	Minor arc $=24$ cm; major arc $=60$ cm; the smaller region is the minor segment; the larger region is the major sector	4	There are $2+5=7$ ratio parts, so each part is $84\div7=12$ cm. The arcs are therefore $2\times12=24$ cm and $5\times12=60$ cm. The smaller region bounded by chord $AB$ and its arc is the minor segment. The larger region bounded by radii $OA$ , $OB$ and the major arc is the major sector.

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2024-11	2H	Q18	3	Allowed	Higher	QP MS
2024-06	3F	Q10	2	Allowed	Foundation	QP MS
2023-06	1F	Q6	1	Non-calculator	Foundation	QP MS
2024-06	3H	Q21	4	Allowed	Higher	QP MS
2023-06	2H	Q12	4	Allowed	Higher	QP MS
2019-06	3H	Q22	4	Allowed	Higher	QP MS
2019-11	3F	Q10	2	Allowed	Foundation	QP MS
2022-06	2F	Q8	4	Allowed	Foundation	QP MS

Other points in G Geometry and measures

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