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Browse Circles, arcs & sectors
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 sector of a circle of radius
12
12
12
cm. The angle of the sector is
75
°
75°
75°
.
O
12 cm
75°
Diagram NOT accurately drawn
(a)
Work out the arc length of the sector. Give your answer correct to 1 decimal place.
(b)
Work out the area of the sector. Give your answer correct to 1 decimal place.
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●●
Level 3
4 marks
Start
→
Mark as done
The diagram shows a sector of a circle of radius
8
8
8
cm. The angle of the sector is
135
°
135°
135°
.
O
8 cm
135°
Diagram NOT accurately drawn
Work out the perimeter of the sector. Give your answer correct to 1 decimal place.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
A sector of a circle has radius
9
9
9
cm and angle
40
°
40°
40°
.
(a)
Work out the arc length of the sector. Give your answer in terms of
π
\pi
π
.
(b)
Work out the area of the sector. Give your answer in terms of
π
\pi
π
.
●●●
●●
Level 3
4 marks
Start
→
Mark as done
The diagram shows a sector of a circle of radius
5.2
5.2
5.2
cm. The angle of the sector is
210
°
210°
210°
.
O
5.2 cm
210°
Work out the
perimeter
of the sector. Give your answer correct to 1 decimal place.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
The diagram shows a sector of a circle, centre
O
O
O
, radius
6.5
6.5
6.5
cm. The angle of the sector is
110
°
110°
110°
.
O
6.5 cm
110°
Diagram NOT accurately drawn
(a)
Work out the area of the sector. Give your answer correct to 3 significant figures. (3 marks)
(b)
Work out the arc length of the sector. Give your answer correct to 3 significant figures. (1 mark)
●●●
●●
Level 3
4 marks
Start
→
Mark as done
The diagram shows a sector of a circle, centre
O
O
O
.
The radius of the circle is
8
8
8
cm and the angle of the sector is
140
°
140°
140°
.
O
8 cm
140°
Diagram NOT accurately drawn
Work out the perimeter of the sector.
Give your answer correct to 3 significant figures. (4 marks)
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●●
Level 3
4 marks
Start
→
Mark as done
Here is a plan of a play area.
The play area is a rectangle with a semicircle joined to one side.
15 m
9 m
The whole play area will be covered with bark chippings.
Bark chippings are sold in bags.
Each bag of bark chippings covers an area of
4
4
4
m²
(a)
Work out the number of bags of bark chippings needed.
(4 marks)
It turns out that each bag of bark chippings only covers an area of
3.5
3.5
3.5
m²
(b)
How does this affect your answer to part (a)?
(1 mark)
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●●
Level 3
5 marks
Start
→
Circle theorems
18 questions
Lesson
Not started
Mark as done
P
P
P
,
Q
Q
Q
and
R
R
R
are points on a circle with centre
O
O
O
.
P
Q
PQ
P
Q
is a diameter.
Angle
Q
P
R
=
27
°
QPR = 27°
QP
R
=
27°
.
27°
x
P
Q
R
O
Diagram NOT accurately drawn
Work out the size of the angle marked
x
x
x
. You must give reasons for each stage of your working.
●●●
●●
Level 3
4 marks
Start
→
Mark as done
A
B
C
D
ABCD
A
B
C
D
is a cyclic quadrilateral.
Angle
D
A
B
=
104
°
DAB = 104°
D
A
B
=
104°
and angle
A
B
C
=
88
°
ABC = 88°
A
B
C
=
88°
.
104°
88°
x
y
A
B
C
D
Diagram NOT accurately drawn
(a)
Work out the size of the angle marked
x
x
x
. Give a reason for your answer.
(b)
Work out the size of the angle marked
y
y
y
.
●●●
●●
Level 3
4 marks
Start
→
Mark as done
A
A
A
,
B
B
B
,
C
C
C
and
D
D
D
are points on a circle with centre
O
O
O
.
Angle
A
C
B
=
41
°
ACB = 41°
A
C
B
=
41°
.
41°
x
A
B
C
D
Diagram NOT accurately drawn
(a)
Write down the size of the angle marked
x
x
x
. Give a reason for your answer.
(b)
Work out the size of angle
A
O
B
AOB
A
O
B
. Give a reason for your answer.
●●●
●●
Level 3
4 marks
Start
→
Mark as done
A
A
A
,
B
B
B
and
C
C
C
are points on a circle with centre
O
O
O
.
Angle
O
A
B
=
26
°
OAB = 26°
O
A
B
=
26°
.
26°
x
A
B
C
O
Diagram NOT accurately drawn
(a)
Work out the size of angle
A
O
B
AOB
A
O
B
.
(b)
Work out the size of the angle marked
x
x
x
. Give a reason for your answer.
●●●
●●
Level 3
4 marks
Start
→
Mark as done
A
A
A
,
B
B
B
,
C
C
C
and
D
D
D
are points on a circle.
3x°
(x + 20)°
A
B
C
D
Diagram NOT accurately drawn
Angle
D
A
B
=
3
x
°
DAB = 3x°
D
A
B
=
3
x
°
and angle
B
C
D
=
(
x
+
20
)
°
BCD = (x + 20)°
B
C
D
=
(
x
+
20
)
°
.
Work out the value of
x
x
x
. Give a reason for your answer. (3 marks)
●●●
●●
Level 3
3 marks
Start
→
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
O
B
=
140
°
AOB = 140°
A
O
B
=
140°
.
140°
A
B
C
O
Diagram NOT accurately drawn
(a)
Work out the size of angle
A
C
B
ACB
A
C
B
. Give a reason for your answer. (2 marks)
(b)
Work out the size of angle
O
A
B
OAB
O
A
B
. Give a reason for your answer. (2 marks)
●●●
●●
Level 3
4 marks
Start
→
Mark as done
T
A
TA
T
A
and
T
B
TB
T
B
are tangents to a circle with centre
O
O
O
.
C
C
C
is a point on the circle. Angle
A
T
B
=
64
°
ATB = 64°
A
T
B
=
64°
.
64°
A
B
C
T
O
Diagram NOT accurately drawn
(a)
Work out the size of angle
A
O
B
AOB
A
O
B
. Give reasons for your answer. [2]
(b)
Work out the size of angle
A
C
B
ACB
A
C
B
. Give a reason for your answer. [2]
●●●
●●
Level 3
4 marks
Start
→
Tangents, chords & the alternate segment
14 questions
Lesson
Not started
Mark as done
The diagram shows a circle with centre
O
O
O
and radius
13
13
13
cm.
A
B
AB
A
B
is a chord of length
24
24
24
cm.
24 cm
13 cm
A
B
O
Diagram NOT accurately drawn
Work out the distance from the centre
O
O
O
to the chord
A
B
AB
A
B
.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
P
A
PA
P
A
and
P
B
PB
P
B
are tangents to a circle with centre
O
O
O
.
Angle
A
P
B
=
48
°
APB = 48°
A
P
B
=
48°
.
48°
A
B
P
O
Diagram NOT accurately drawn
(a)
Write down the size of angle
O
A
P
OAP
O
A
P
. Give a reason for your answer.
(b)
Work out the size of angle
A
O
B
AOB
A
O
B
.
●●●
●●
Level 3
4 marks
Start
→
Mark as done
P
A
PA
P
A
is a tangent to a circle with centre
O
O
O
and radius
8
8
8
cm. The point
A
A
A
is where the tangent touches the circle.
O
P
=
17
OP = 17
O
P
=
17
cm.
Work out the length of
P
A
PA
P
A
.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
P
A
PA
P
A
and
P
B
PB
P
B
are tangents to a circle with centre
O
O
O
, touching the circle at
A
A
A
and at
B
B
B
.
P
A
=
9
PA = 9
P
A
=
9
cm.
9 cm
O
A
B
P
Diagram NOT accurately drawn
(a)
Write down the length of
P
B
PB
P
B
. Give a reason for your answer.
(b)
Write down the size of angle
O
A
P
OAP
O
A
P
. Give a reason for your answer.
●●●
●●
Level 3
4 marks
Start
→
Mark as done
T
A
TA
T
A
and
T
B
TB
T
B
are tangents to a circle with centre
O
O
O
.
C
C
C
is a point on the circle. Angle
A
T
B
=
64
°
ATB = 64°
A
T
B
=
64°
.
64°
A
B
C
T
O
Diagram NOT accurately drawn
(a)
Work out the size of angle
A
O
B
AOB
A
O
B
. Give reasons for your answer. [2]
(b)
Work out the size of angle
A
C
B
ACB
A
C
B
. Give a reason for your answer. [2]
●●●
●●
Level 3
4 marks
Start
→