A

Chapter 3: Circles IIPaper 1This test paper contains 20 questions. Answer ALL the questions.The diagrams accompanying the questions are not drawn to scale unless mentioned.You are allowed to use a scientific calculator that cannot be programmed.

1 In the circle shown in Diagram 1, O is the centre and OAB is 35°.

35°

O B

x°

DIAGRAM 1Find the value of x.A 35B 45C 55D 65

2 In the circle in Diagram 2, O is the centre of the circle and ABC is 27°.

27°

y°

A

C

DIAGRAM 2

Find the value of y.A 293 C 306B 296 D 333

1

B

X

3 In Diagram 3, AB and XY are straight lines, and O is the centre of the circle. AXY = 54° and XYB = 22°.

54°

x°A B

O

22°

Y

DIAGRAM 3

Find the value of x.A 98B 100C 102D 104

4 In the circle shown in Diagram 4, O is the centre of the circle. AOB and CD are straight lines.

A D

y° 38°

O

C

B

DIAGRAM 4

If CDB = 38°, find the value of x + y.A 76B 96C 114D 124

2

x°

5 In Diagram 5, O is the centre of the circle and XOY = 80°.

O 80°

X Y

DIAGRAM 5

Find the value of x + y.A 40B 60C 70D 80

6 In Diagram 6, O is the centre of the circle and AOB is 126°.

A

126°

x° B

DIAGRAM 6

Determine the value of x.A 54

3

O

y° x°

C X

B 117C 126D 234

7 In Diagram 7, O is the centre of the circle and AXY and BOXC are straight lines.

A

42°

O Y

BDIAGRAM 7

If BAY = 42°, find the value of OYC.A 42°B 46°C 48°D 50°

8 In Diagram 8, AOB and XOY are diameters of the circle.

A

O X Y

88°

4

BDIAGRAM 8

If YOB = 88°, find the value of AXO.A 46°B 72°C 88°D 92°

9 In Diagram 9, ABCD is a cyclic quadrilateral. BED and AEC are straight lines and BAE = 36°.

B C

94° 78°

E 36°

x°A

D

DIAGRAM 9

Given that ABC = 94° and DCB = 78°, find the value of x.A 64B 68C 70D 72

10 In Diagram 10, PQST and PRST are cyclic quadrilaterals.

T

S P 96°

25°

5

x°

70°

Q

R

DIAGRAM 10

If RPT = 96°, QSR = 25°, and PQS = 70°, find the value of x.A 49B 59C 64D 69

6

11 In Diagram 11, POR and QOS are straight lines, and O is the centre of the circle.

O Q S

y°

58°

P T DIAGRAM 11

If QTR = 58°, find the value of y.A 58B 60C 62D 64

12 In Diagram 12, XBC = 135° and YZX = 50°.

C B

135°

A

X

Y 50°

Z

DIAGRAM 12

7

R

Find the value of AXB.A 60°B 70°C 80°D 85°

13 Diagram 13 shows a circle with centre O. ABC is an isosceles triangle.

A

40°

O

C B

DIAGRAM 13

If BAC = 40°, find the value of ABO.A 20°B 25°C 30°D 35°

14 In Diagram 14, AOB and XOY are straight lines that intersect at O, the centre of the circle.

Y

x°

136°

A B O

y°

X

8

DIAGRAM 14

If AOY = 136°, find the value of x + y.A 76B 80C 86D 90

15 In Diagram 15, O is the centre of the circle, and AOB and COE are straight lines.

C

x°

B

40°

A

D 62°

E

DIAGRAM 15

If CAB = 40° and DEC = 62°, find the value of x.A 12B 14C 16D 18

16 In Diagram 16, ABCD is a cyclic quadrilateral and AD = DC.

C

32°

9

O

D

36°

A x°

B

DIAGRAM 16

If DAC = 36° and ACB = 32°, find the value of x.A 72B 74C 76D 80

17 Diagram 17 shows a circle with centre O. AOB and XYZ are straight lines.

A

Z 32°

O

Y 118°

p° X

BDIAGRAM 17

If BYZ = 118° and BAX = 32°, find the value of p.A 30

10

B 32C 48D 60

18 In Diagram 18, O is the centre of the circle and BOD is a straight line.

B C

26°

O

4x°

AD

DIAGRAM 18

If ACD = 26°, and AOB = 4x, find the value of x.A 32B 38C 68D 128

19 In Diagram 19, ABCD is a cyclic quadrilateral. AOM is a straight line and O is the centre of the circle.

B

MO y°

C A

DDIAGRAM 19

If ADC = 116°, find the value of y. A 48

11

116°

B 50C 52D 54

20 In Diagram 20, AB is the diameter of the circle, and O is the centre.

E

O BA

78° C

D DIAGRAM 20

If DOC = 78°, and COB = 36°, find the value of y.A 22B 23C 32D 33

12

36°

y°

Paper 2This test paper contains 10 questions. Answer ALL the questions.The diagrams accompanying the questions are not drawn to scale unless mentioned.You are not allowed to use a calculator.

1 In Diagram 1, ABCD is a cyclic quadrilateral, where ADC = 92° and AB = BC.

y A

C

92°

D

DIAGRAM 1

Find the value of y.

2 In Diagram 2, O is the centre of the circle and ACB = 38°.

C

O 38°

B

A

DIAGRAM 2

Find the value of OBA.

13

B

3 In Diagram 3, M is the centre of the circle and AB and CD are parallel lines.

B 50°

A

M x

D

C

DIAGRAM 3

If ABM is 50°, find the value of x.

4 In Diagram 4, O is the centre of the circle and ABC = 152°.

B

152°

A C O

b a

D DIAGRAM 4

Find the value of a + b.

14

5 In Diagram 5, AOC is the diameter of the circle.

27° 35°

O A C

114° y D

F E DIAGRAM 5

If FEB = 114°, ABE = 27° and DBC = 35°, find the value of y.

6 In Diagram 6, O is the centre of the circle and AX is the diameter. XY is parallel to BA.

A

y

Y O

72° B

XDIAGRAM 6

If XOB = 72°, find the value of y.

15

B

7 In Diagram 7, O is the centre of the circle. QOR is a straight line.

S

y

O P 64°

22°

QDIAGRAM 7

If POQ = 64° and OQS = 22°, find the value of y.

8 In Diagram 8, O is the centre of the circle. ACX and BCY are straight lines.

Y

36° X

OC

y A B

DIAGRAM 8

If YCX = 36°, find the value of y.

16

R

9 In Diagram 9, VXZ is a triangle and VWYU is a cyclic quadrilateral.

72°

W 114°U

x 53°

X Y Z

DIAGRAM 9

If VWY = 114°, VZY = 53° and XVZ = 72°, find the value of x.

10 In Diagram 10, O is the centre of the circle and DOE is a straight line.

C

22°

O D E

y 86°

A B

DIAGRAM 10

If AOB = 86° and ACD = 22°, find the value of y.

17

V