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Circle Properties
Question Paper 1
Level
Subject
IGCSE
Maths
Exam Board
Topic
Sub Topic
Booklet
Edexcel
Shape, Space and Measures
Circle properties
Question Paper 1
60 minutes
Time Allowed:
Score:
/50
Percentage:
/100
Grade Boundaries:
9
8
7
6
5
4
3
2
1
>90%
80%
70%
60%
50%
40%
30%
20%
10%
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1
C
Diagram NOT
accurately drawn
106°
D
57°
B
O
A
A, B, C and D are points on a circle, centre O.
Angle ADB = 57°.
Angle BCD = 106°.
(a) (i) Calculate the size of angle AOB.
°
.................. . . . . . . . . . . . . . . . . . . . . .
(ii) Give a reason for your answer.
. . . . . . .................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................................................................................... . . . . .. . . . . . . . . . . . . . . . . . .
. . . . . . .................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................................................................................... . . . . .. . . . . . . . . . . . . . . . . . .
(2)
(b) Calculate the size of angle BAD.
°
.................. . . . . . . . . . . . . . . . . . . . . .
(1)
(Total for Question 1 is 3 marks)
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2
Q
R
41°
Diagram NOT
accurately drawn
T
34°
P
S
P, Q, R and S are points on the circumference of a circle.
PR and QS intersect at T.
Angle QPR = 34° and angle PRS = 41°
(a) (i) Find the size of angle PQS.
......................................... . . . . . . . . . . . . . . . . . . . .
°
(ii) Give a reason for your answer.
. . . . . . ..................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . .. . . . . . . . . . . . . . . . . . .
. . . . . . ..................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . .. . . . . . . . . . . . . . . . . . .
(2)
(b) (i) Find the size of angle PTS.
......................................... . . . . . . . . . . . . . . . . . . . .
°
(ii) Explain why T cannot be the centre of the circle.
. . . . . . ..................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . .. . . . . . . . . . . . . . . . . . .
. . . . . . ..................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . .. . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 2 is 4 marks)
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3
D
Diagram NOT
accurately drawn
O
8 cm
A
C
63°
30°
B
B, C and D are points on a circle, centre O.
BOD is a diameter of the circle.
AB is the tangent to the circle at B.
AO = 8 cm.
Angle BAO = 30°
Angle CBD = 63°
Calculate the length of BC.
Give your answer correct to 3 significant figures.
................................................. . . . . . . . . . . . . . .
(Total for Question 3 is 4 marks)
cm
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4
D
Diagram NOT
accurately drawn
C
A
|
x°
|
69°
O
B
E
A, B, C and D are points on a circle, centre O.
AOBE and DCE are straight lines.
CO = CE.
Angle AOD = 69°
Angle CEO = x°
Calculate the value of x.
Show your working clearly.
x = ..................................... . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 4 is 6 marks)
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5
O
5.4 cm
Diagram NOT
accurately drawn
5.4 cm
72°
A
B
P
The diagram shows a sector OAPB of a circle, centre O.
AB is a chord of the circle.
OA = OB = 5.4 cm.
Angle AOB = 72°
Calculate the area of the shaded segment APB.
Give your answer correct to 3 significant figures.
.................................................. . . . . . . . . . . . . .
(Total for Question 5 is 5 marks)
cm2
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6
Diagram NOT
accurately drawn
B
C
A
58°
O
D
A, B, C and D are four points on a circle, centre O.
AD is a diameter of the circle.
Angle BAD = 58°
(a) Calculate the size of angle ADB.
°
......................................... . . . . . . . . . . . . . . . . . . . . .
(2)
(b) (i) Calculate the size of angle BCD.
°
......................................... . . . . . . . . . . . . . . . . . . . . .
(ii) Give a reason for your answer.
(2)
(Total for Question 6 is 4 marks)
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7
Diagram NOT
accurately drawn
A
7 cm
B
5 cm
28°
D
C
6 cm
X
A, B, C and D are four points on a circle.
ABX and DCX are straight lines.
AB = 7 cm, BX = 5 cm and CX = 6 cm.
Angle BXC = 28°
(a) Calculate the length of AC.
Give your answer correct to 3 significant figures.
.................................................. . . . . . . . . . . . .
cm
(3)
(b) Calculate the length of DC.
................................................ . . . . . . . . . . . . . .
cm
(3)
(Total for Question 7 is 6 marks)
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8
B
Diagram NOT
accurately drawn
P
O
C
76°
A
A, B and C are points on a circle, centre O.
Angle ACB = 76°
PA and PB are tangents to the circle.
Calculate the size of angle APB.
°
......................................... . . . . . . . . . . . . . . . . . . . . .
(Total for Question 8 is 4 marks)
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9
C
103°
B
Diagram NOT
accurately drawn
D
39°
P
A
A, B, C and D are points on a circle.
PA is a tangent to the circle.
Angle PAD = 39°
Angle BCD = 103°
Calculate the size of angle ADB.
°
................... . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 9 is 3 marks)
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10 PTR and QTS are chords of a circle.
Q
Diagram NOT
accurately drawn
P
PT = 3 cm.
ST = 10 cm.
x cm
3 cm
RT = 15 cm.
T
QT = x cm.
10 cm
15 cm
S
R
Calculate the value of x.
x = ......................................................
(Total for Question 10 is 2 marks)
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12
Diagram NOT
accurately drawn
O
B
26q
A
P
A and B are points on a circle, centre O.
PA is the tangent to the circle at A.
OBP is a straight line.
Angle APO = 26q
Calculate the size of angle ABP.
....... . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 12 is 3 marks)
q