CIRCLEG_SeriesK2_S

Circle Geometry  n t

 S t ude

Book  - Ser ies K  2  -

Mathlecs Instant Workbooks

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Circle geometry Student Book - Series K 2 Contents Topics

Date completed

Topic 1 - Chord properties of a circle

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Topic 2 - Angle properties of a circle

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Topic 3 - Tangent properties of a circle

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Topic 4 - Cyclic quadrilaterals

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Topic 5 - The angle in the alternate segment

 __/__/__ 

Topic 6 - Further properties of a circle

 __/__/__ 

Topic 7 - Deductive exercises related to the circle

 __/__/__ 

Topic 8 - Miscellaneous questions

 __/__/__ 

Practice Tests Topic 1 - Topic test A

 __/__/__ 

Topic 2 - Topic test B

 __/__/__ 

Author of The Topics and Topic Tests: AS Kalra

Circle geometry Mathletics Instant Workbooks – Series K 2 Copyright © 3P Learning

ii

Circle geometry Topic 1 - Chord properties of a circle

1

QUESTION

Find the value of the pronumeral in the following questions.

a

b

c M

A

B

B

 y

O

O O

M

 x

A

a

M

B A

AB = 18 cm

___________

2

QUESTION

AB = 36 cm

___________

Find the value of the pronumeral in the following questions.

a

b

c M

A

B

 y°

O

O

O

 x°

A

___________

AB = 12.6 cm

M

B

a°

M

B A

AM = BM = 5 cm

QUESTION

3

AM = BM = 8 cm

___________

b

C

c

C A

C

D 50°

O  x° 85°

 y°

O a °

A

B

120°

O

D

D B

B AB = CD = 9 cm

QUESTION

___________

Find the value of the pronumeral.

a

A

AM = BM = 12 cm

___________

4

a

AB = CD = 6 cm

___________

___________

AB = CD = 12 cm

___________

Find the value of the pronumeral in the following. b

C

c

A

C

C

A O  x

θ

θ

O D

A

110° 110° O

75°  y

75° B

D

B

a

D

B

___________

CD = 5 cm

QUESTION a

5

b C

A

A

N

M M

D

B

O

O

O

AB = CD

AB = CD

OM = 6 cm

ON = 9 cm

Find ON.

___________

C

c

D

N

N

M

AB = 12 cm

Find the value of the required length.

C

A

___________

AB = 7 cm

___________

Find OM.

B

B

D

OM = ON = 7 cm

___________

CD = 21 cm Find AB.

___________

Circle geometry Mathletics Instant Workbooks – Series K 2 Copyright © 3P Learning

1

Circle geometry Topic 2 - Angle properties of a circle

1

QUESTION a

Find the value of the pronumeral in each of the following. b

C

c

C

C

a

°

O

m°

O A

80°

A

140°

B

___________  y

B

A

___________ e

C

___________ f

°

 x

°

n

°

m

°

 y

°

B

A 180°

30°

70°

___________

2

QUESTION

___________

b °

___________

Find the value of the pronumeral in the following.

a a

c a

°

30°

 x°

40°

35°

b

°

___________ d

15°

 y°

___________ e

m

°

60°

B

d

 x

O

f y

 x

°

°

___________

°

n

°

___________

QUESTION

3

___________

___________

Find the value of the pronumeral in the following.

a

b  x

°

c a

b

°

240° 220°

___________

b

°

70° a°

a

°

120°

b

°

110°

°

___________

___________

Circle geometry Mathletics Instant Workbooks – Series K 2 Copyright © 3P Learning

2

Circle geometry Topic 3 - Tangent properties of a circle QUESTION

1

Find the value of the pronumeral.

a

b

c

T

P O

x

°

O

T

P

a

°

O

P  y

°

T

______________________ QUESTION

2

______________________

______________________

Find the value of the pronumeral.

a

b

c

O

T m°

O

a

°

T

O 60°

55°

 x °

P

40

°

T

P

P

______________________ QUESTION

3

______________________

______________________

Find the value of the pronumeral.

a

b

c

Q

Q

b cm c

cm

T P 14 cm

a

Q cm

P

T

______________________ QUESTION

4

T

21 cm

9 cm

P

______________________

______________________

Find the value of the pronumeral.

a

Q

b

c

m

°

7 cm a

Q °

n°

T

 p°

65

P

P

60

°

10 cm

T

 y

°

20 cm

P

 x

50

Q

T

______________________ QUESTION

5

______________________

______________________

Find the value of the pronumeral.

a

b

c l

°

a 40

°

°

°

c

°

b

 y

n

50

°

m

°

°

______________________

______________________

 p

°

°

 x

°

60

°

______________________

Circle geometry Mathletics Instant Workbooks – Series K 2 Copyright © 3P Learning

3

Circle geometry Topic 4 - Cyclic quadrilaterals QUESTION

1

Find the value of the pronumeral.

a

b

c 110°

88°

a

°

 x

°

65°

 y

°

______________________ d

______________________ e

 p

f 91°

°

m

°

°

2

°

b

85°

105°

°

86°

n

°

______________________ QUESTION

a

87°

q 60°

______________________

______________________

______________________

Find the value of the pronumeral.

a

b

c 85°

 x

°

n  y

°

°

110°

m

°

120°

b

°

a

°

______________________ d

______________________ e

a

°

b

°

f  x

°

°

°

b°

a°

115°

75°

89°

______________________

3

80° c°

a

 y

105°

QUESTION

______________________

______________________

______________________

Find the value of the pronumeral.

a

 y

b

°

c a

°

m

°

97°

 x

°

 p

105°

°

b n

97°

______________________

°

93°

______________________

°

c

°

80°

______________________

Circle geometry Mathletics Instant Workbooks – Series K 2 Copyright © 3P Learning

4

Circle geometry Topic 5 - The angle in the alternate segment QUESTION

1

Find the value of the pronumeral.

a

b 50°

c

A

A

P

m

°

a

B

°

°

T

B

A

P

B

 x

T 30° P

T

45°

______________________

______________________

______________________

______________________

______________________

______________________

d

e

f

A

n

°

48° 60°

B

50°

 y

°

35°

70°

 p

°

70°

 x

°

m

°

 y

°

 x

°

T

P

______________________

______________________

______________________

______________________

______________________

______________________

QUESTION

2

Find the value of the pronumeral.

a

b  x°  y°

65°

c

°

20° 135°

c 80°

50°

 x

°

a

70°

b

°

°

 y

°

______________________

______________________

______________________

______________________

______________________

______________________

d

e

f a

75°

a

b

°

°

°

n

°

m

°

40°

80° 55°

b

°

______________________

______________________

______________________

______________________

______________________

______________________

Circle geometry Mathletics Instant Workbooks – Series K 2 Copyright © 3P Learning

5

Circle geometry Topic 6 - Further properties of a circle QUESTION

1

Find the value of the pronumeral. All measurements are in centimetres.

a

C

b

B

B

 y

C

______________________

10

 x

E

15

A

A

______________________

3 D

d

a

QUESTION

A

______________________

12

______________________

C

2

E

m

6

4

A

______________________

8

______________________

B

______________________ D

______________________ 16 E

______________________

D

D 20

E 8

______________________ c

______________________

2 8

______________________

B C

Find the value of the pronumeral. All measurements are in centimetres.

a

b 5

A

B D

B 9

 x 

E

2

A

4

E

 y

D 3

2 C

C

_____________________________________

_____________________________________

_____________________________________

_____________________________________

C

c

d D

7

D

C

6

E

7

m

3 E

a

2

A

B

A

8

B

_____________________________________

_____________________________________

_____________________________________

_____________________________________

QUESTION

3

Find the value of the pronumeral. All measurements are in centimetres. P

a

b

 x

T

P

4 a

Q 5 T

R

4

21 Q

R

_____________________________________

_____________________________________

_____________________________________

_____________________________________

Circle geometry Mathletics Instant Workbooks – Series K 2 Copyright © 3P Learning

6

Circle geometry Topic 7 - Deductive exercises related to the circle QUESTION 1

Find the value of the pronumeral.

a

b

50

°

C A

a

O

 x

°

°

40

°

D

B

_____________________________________

_____________________________________

_____________________________________

_____________________________________

_____________________________________

_____________________________________

c

d

R

A

C O

70

°

O a

°

a°

b

°

P

B 38°

C

Q

_____________________________________

_____________________________________

_____________________________________

_____________________________________

_____________________________________

_____________________________________

QUESTION 2

Find the value of the pronumeral.

a

b

C

C

B

46

°

A

°

55

°

°

°

m D

 x y 60 O

°

B

A

_____________________________________

_____________________________________

_____________________________________

_____________________________________

_____________________________________

_____________________________________

c

d c

°

a

b

 y

68

°

°

°

 x

75

°

°

55

°

°

_____________________________________

_____________________________________

_____________________________________

_____________________________________

_____________________________________

_____________________________________

Circle geometry Mathletics Instant Workbooks – Series K 2 Copyright © 3P Learning

7

Circle geometry Topic 8 - Miscellaneous questions QUESTION

1

Find the value of the pronumeral.

a

b

c

 x

B

M

85° D

B

AM = BM = 12 cm

______________________

2

O  x°

a°

A

B

M AB = 16 cm

QUESTION

C

O

O

A

A

______________________

______________________

Find the value of the pronumeral. C

a

b

c a

m°

°

50

 x

°

°

b

°

O

O

96° B A

______________________ QUESTION

3

______________________

______________________

Find the value of the pronumeral.

a

b

c

Q 9 cm

O

O

T 70

°

 y

°

 x cm

a°

P

P

T

______________________ QUESTION

4

______________________

______________________

Find the value of the pronumeral.

a

b

n 110 °

c  y°

°

m°

m

°

65

°

 x°

______________________ QUESTION

5

110°

95°

______________________

n°

______________________

Find the value of the pronumeral.

a

b  x

°

c  x

 y

°

4

12 16

3

 x

5 4

75

°

30

°

______________________

______________________

______________________

Circle geometry Mathletics Instant Workbooks – Series K 2 Copyright © 3P Learning

8

Circle geometry Topic Test Instructions

PART A This part consists of 10 multiple-choice questions Each question is worth 1 mark Attempt ALL questions Calculators are NOT to be used Fill in only ONE CIRCLE for each question

Time allowed: 15 minutes

Total marks = 10 Marks

1

The distance around a circle is called the A

2

45

°

B

90

°

C

180

D

270

1

D

360

1

°

°

90

°

B

180

°

C

270

°

°

45

°

B

90

°

C

135

D

170

1

3

D

infinite

1

diameter

D

tangent

1

°

°

1

B

2

C

chord

B

radius

C

1

B

2

C

D

3

4

1

semicircles

B

cyclics

C

concentric

D

none of these

1

A straight line that touches a circle at one point only is called the A

10

1

Circles of different radii which have a common centre are called A

9

secant

The maximum number of points in which a straight line can cut a circle are A

8

D

The axis of symmetry of a circle is called a A

7

radius

The number of diameters a circle has, equals A

6

C

The angle between the tangent and the radius through the point of contact is A

5

circumference

The opposite angles of a cyclic quadrilateral add up to A

4

B

The angle in a semicircle is equal to A

3

diameter

radius

B

diameter

C

tangent

D

secant

1

bisect

D

none of these

1

The tangents at the ends of any diameter are A

perpendicular

B

parallel

C

Total marks achieved for PART A

10

Circle geometry Mathletics Instant Workbooks – Series K 2 Copyright © 3P Learning

9

Circle geometry Topic Test Instructions

PART B

This part consists of 15 questions Each question is worth 1 mark Attempt ALL questions Calculators may be used

Time allowed: 20 minutes

Total marks = 15

Questions

2

Marks

___________________

1

___________________

1

C

A circle has centre O and COD is a straight line. 1

Answers only

60°

Find the size of the obtuse angle AOB.

O B

What is the size of  ∠DAC?

A D

Complete the following sentences. 3

Equal chords are . . . . . . . . from the centre.

___________________

1

4

Equal chords make . . . . . . . . angles at the centre.

___________________

1

5

A line from the centre of a circle, perpendicular to a chord, . . . . . . . the chord.

___________________

1

The right bisector of any chord of a circle passes through the . . . . . . . .

___________________

1

The angle at the centre of a circle is . . . . . . . . the angle at the circumference standing on the same arc.

___________________

1

8

The angle in a semicircle is a . . . . . . . .

___________________

1

9

Angles in the same segment of a circle are . . . . . . . .

___________________

1

10

The opposite angles of a cyclic quadrilateral are . . . . . . . .

___________________

1

11

The angle between a tangent and the radius through its point of contact is always equal to . . . . . . . .

___________________

1

The tangents drawn to a circle from an external point are . . . . . . . . in length.

___________________

1

13

The tangents at the end of any diameter are . . . . . . . .

___________________

1

14

The line from the centre of a circle to the midpoint of a chord meets the chord at . . . . . . . . angles.

___________________

1

When two circles intersect, the line joining their centres  bisects the common chord at . . . . . . . . angles.

___________________

1

6

7

12

15

Total marks achieved for PART B

15

Circle geometry Mathletics Instant Workbooks – Series K 2 Copyright © 3P Learning

10