igureMaths
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Circles, arcs & sectors
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48 questions at your level
Difficulty
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Level 2
Level 3
Level 4
Level 5
Arc length & sector area
20 questions
Lesson
Not started
Mark as done
The diagram shows a circle of radius
10
10
10
cm. A chord divides the circle, and the angle at the centre is
80
°
80°
80°
.
O
10 cm
80°
Diagram NOT accurately drawn
Work out the area of the shaded segment. Give your answer correct to 1 decimal place.
●●●●●
Level 5
4 marks
Start
→
Mark as done
A circle has radius
7
7
7
cm. The minor arc
A
B
AB
A
B
has length
6.5
6.5
6.5
cm.
(a)
Work out the angle of the minor sector
O
A
B
OAB
O
A
B
. Give your answer correct to 1 decimal place.
(b)
Work out the area of the
major
sector. Give your answer correct to 3 significant figures.
●●●●●
Level 5
5 marks
Start
→
Mark as done
The diagram shows a circle, centre
O
O
O
, radius
r
r
r
cm, and two regular octagons.
r cm
O
The sides of the larger octagon are tangents to the circle.
The vertices of the smaller octagon lie on the circle.
By considering perimeters, show that
4
2
−
2
<
π
<
8
(
2
−
1
)
4\sqrt{2 - \sqrt{2}} < \pi < 8(\sqrt{2} - 1)
4
2
−
2
<
π
<
8
(
2
−
1
)
(4 marks)
●●●●●
Level 5
4 marks
Start
→
Circle theorems
18 questions
Lesson
Not started
Mark as done
A
A
A
,
B
B
B
and
C
C
C
are points on a circle with centre
O
O
O
.
Angle
A
C
B
=
58
°
ACB = 58°
A
C
B
=
58°
.
58°
x
A
B
C
O
Diagram NOT accurately drawn
Work out the size of the angle marked
x
x
x
(angle
O
A
B
OAB
O
A
B
). You must give reasons for each stage of your working.
●●●●●
Level 5
4 marks
Start
→
Mark as done
A
A
A
,
B
B
B
,
C
C
C
and
D
D
D
are points on a circle. The chords
A
C
AC
A
C
and
B
D
BD
B
D
cross at the point
E
E
E
.
Angle
A
D
B
=
40
°
ADB = 40°
A
D
B
=
40°
and angle
D
B
C
=
33
°
DBC = 33°
D
B
C
=
33°
.
40°
x
33°
A
B
C
D
E
Diagram NOT accurately drawn
(a)
Write down the size of angle
A
C
B
ACB
A
C
B
. Give a reason for your answer.
(b)
Work out the size of angle
A
E
B
AEB
A
E
B
, marked
x
x
x
.
●●●●●
Level 5
4 marks
Start
→
Mark as done
P
P
P
,
Q
Q
Q
and
R
R
R
are points on a circle, centre
O
O
O
.
S
P
T
SPT
S
P
T
is the tangent to the circle at
P
P
P
.
67°
49°
O
P
Q
R
T
S
Angle
T
P
Q
=
67
°
TPQ = 67°
T
P
Q
=
67°
Angle
R
P
S
=
49
°
RPS = 49°
R
P
S
=
49°
Work out the size of angle
O
Q
R
OQR
O
QR
.
Write down any circle theorems that you use.
(4 marks)
●●●●●
Level 5
4 marks
Start
→
Tangents, chords & the alternate segment
14 questions
Lesson
Not started
Mark as done
A
A
A
,
B
B
B
and
C
C
C
are points on a circle.
T
A
TA
T
A
is a tangent to the circle at
A
A
A
.
Angle
T
A
B
=
58
°
TAB = 58°
T
A
B
=
58°
and
C
A
=
C
B
CA = CB
C
A
=
C
B
.
58°
x
A
B
C
T
Diagram NOT accurately drawn
(a)
Write down the size of angle
A
C
B
ACB
A
C
B
, marked
x
x
x
. Give a reason for your answer.
(b)
Work out the size of angle
C
A
B
CAB
C
A
B
. Give a reason for your answer.
●●●●●
Level 5
4 marks
Start
→
Mark as done
A circle has centre
O
O
O
. The chord
A
B
AB
A
B
has length
16
16
16
cm, and the perpendicular distance from
O
O
O
to
A
B
AB
A
B
is
6
6
6
cm.
16 cm
6 cm
O
A
B
Diagram NOT accurately drawn
(a)
Work out the radius of the circle.
The point
P
P
P
is
26
26
26
cm from
O
O
O
.
P
T
PT
P
T
is a tangent to the circle, touching it at
T
T
T
.
(b)
Work out the length
P
T
PT
P
T
.
●●●●●
Level 5
5 marks
Start
→
Mark as done
R
R
R
and
S
S
S
are points on a circle, centre
O
O
O
.
The tangent to the circle at
R
R
R
and the tangent to the circle at
S
S
S
meet at the point
T
T
T
.
O
R
S
T
Prove that
R
T
=
S
T
RT = ST
R
T
=
S
T
(4 marks)
●●●●●
Level 5
4 marks
Start
→
Mark as done
P
P
P
,
Q
Q
Q
and
R
R
R
are points on a circle, centre
O
O
O
.
S
P
T
SPT
S
P
T
is the tangent to the circle at
P
P
P
.
67°
49°
O
P
Q
R
T
S
Angle
T
P
Q
=
67
°
TPQ = 67°
T
P
Q
=
67°
Angle
R
P
S
=
49
°
RPS = 49°
R
P
S
=
49°
Work out the size of angle
O
Q
R
OQR
O
QR
.
Write down any circle theorems that you use.
(4 marks)
●●●●●
Level 5
4 marks
Start
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