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Copyright ©
Student Book - Series K-2
Circle Geometry
Mathletics Instant
Workbooks
Circle geometryStudent Book - Series K 2
Contents
Topics
Topic 1 - Chord properties of a circle __/__/__ Date completed
Topic 2 - Angle properties of a circle __/__/__ Topic 3 - Tangent properties of a circle __/__/__ Topic 4 - Cyclic quadrilaterals __/__/__ Topic 5 - The angle in the alternate segment __/__/__
Topic 7 - Deductive exercises related to the circle __/__/__
Topic 6 - Further properties of a circle __/__/__
Topic 8 - Miscellaneous questions __/__/__
Author of The Topics and Topic Tests: AS Kalra
Practice Tests
Topic 1 - Topic test A __/__/__ Topic 2 - Topic test B __/__/__
Circle geometryMathletics Instant Workbooks – Series K 2 Copyright © 3P Learning ii
Circle geometry
Circle geometryMathletics Instant Workbooks – Series K 2 Copyright © 3P Learning 1
Topic 1 - Chord properties of a circle
67Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)CHAPTER 8
UNIT 1: Chord properties of a circle
EXCEL YEARS 9 & 10 ADVANCED MATHS
Pages 210–212
QUESTION 1 Find the value of the pronumeral in the following questions.
a b c
___________ ___________ ___________
QUESTION 2 Find the value of the pronumeral in the following questions.
a b c
___________ ___________ ___________
QUESTION 3 Find the value of the pronumeral.
a b c
___________ ___________ ___________
QUESTION 4 Find the value of the pronumeral in the following.
a b c
___________ ___________ ___________
QUESTION 5 Find the value of the required length.
a b c
___________ ___________ ___________
AB = 18 cm
A B
O
Mx
AB = 36 cm
A B
O
My
AB = 12.6 cm
A
B
OM
a
AM = BM = 5 cm
A B
O
Mx°
AM = BM = 8 cm
A B
O
My°
AM = BM = 12 cm
A
B
O
M
a°
AB = CD = 9 cm
A
B
O
C
x°
D85°
AB = CD = 6 cm
A
B O
C
y°
D50°
AB = CD = 12 cm
A
B
O
C
a°
D
120°
CD = 5 cm
A
B
O
C
xD
θθ
AB = 12 cm
A
B
O
C
a
D
110° 110°
AB = CDOM = 6 cmFind ON.
A
B
O
C
D
M N
AB = CDON = 9 cmFind OM.
A
B
O
CD
M
N
OM = ON = 7 cmCD = 21 cm
Find AB.
A
B
O
C
D
M
N
AB = 7 cm
A
B
O
C
y
D75°
75°
Circle geometry
Circle geometryMathletics Instant Workbooks – Series K 2 Copyright © 3P Learning 2
68 EXCEL ESSENTIAL SKILLS: YEAR 10 MATHS REVISION AND EXAM WORKBOOK 2 – EXTENSION
Circle geometry (OPTION 5)UNIT 2: Angle properties of a circle
EXCEL YEARS 9 & 10 ADVANCED MATHS
Pages 213–214
QUESTION 1 Find the value of the pronumeral in each of the following.
a b c
___________ ___________ ___________
d e f
___________ ___________ ___________
A B
O
C
a°
80°
QUESTION 2 Find the value of the pronumeral in the following.
a b c
___________ ___________ ___________
d e f
___________ ___________ ___________
QUESTION 3 Find the value of the pronumeral in the following.
a b c
___________ ___________ ___________
A
B
O
C
m°
140°
A B
O
C
x°
60°
A B
C
y°
180°
m°
70°
n°y°30°
x°
a° 30° a° 40°b°
x°35°
y°15°
m° y°x°
n°
x°
220°
b°
120°
a°240°
b°70° a°
110°
b°
a°
Topic 2 - Angle properties of a circle
Circle geometry
Circle geometryMathletics Instant Workbooks – Series K 2 Copyright © 3P Learning 3
69Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)UNIT 3: Tangent properties of a circle
EXCEL YEARS 9 & 10 ADVANCED MATHS
Pages 216–217
QUESTION 1 Find the value of the pronumeral.
a b c
______________________ ______________________ ______________________
QUESTION 2 Find the value of the pronumeral.
a b c
______________________ ______________________ ______________________
QUESTION 3 Find the value of the pronumeral.
a b c
______________________ ______________________ ______________________
QUESTION 4 Find the value of the pronumeral.
a b c
______________________ ______________________ ______________________
QUESTION 5 Find the value of the pronumeral.
a b c
______________________ ______________________ ______________________
O x°P
T
O
y°P
T
Oa°P
T
O
a°
P T40°
O
x°
P
T55°
Om°
P
T
60°
T
a cmP Q
14 cm
T
b cm
P
Q
21 cm T
c cm
P
Q
9 cm
40°
a°
b°
c° 50°n°
l°
m° 60°
p°
x°
y°
Tx
P
Q
10 cm65°p°
T
yP
Q
7 cm
60°
m°
T
a
P
Q20 cm
50°
n°
Topic 3 - Tangent properties of a circle
Circle geometry
Circle geometryMathletics Instant Workbooks – Series K 2 Copyright © 3P Learning 4
70 EXCEL ESSENTIAL SKILLS: YEAR 10 MATHS REVISION AND EXAM WORKBOOK 2 – EXTENSION
Circle geometry (OPTION 5)UNIT 4: Cyclic quadrilaterals
EXCEL YEARS 9 & 10 ADVANCED MATHS
Pages 214–216
QUESTION 1 Find the value of the pronumeral.
a b c
______________________ ______________________ ______________________
d e f
______________________ ______________________ ______________________
QUESTION 2 Find the value of the pronumeral.
a b c
______________________ ______________________ ______________________
d e f
______________________ ______________________ ______________________
QUESTION 3 Find the value of the pronumeral.
a b c
______________________ ______________________ ______________________
88°x°
110°
y° 65°a°
60°
p°
105°
q°
91°m°
85°n°
87°b°
86°
a°
120°y°
x° 85°
b°a°
110°m°
n°
105°
b°a°
115°
y° a°
89°
x°
97°
y°
x°105°
97°p°
m°
93°n°b°
a°
80°c°
75°
b°a°
80°c°
Topic 4 - Cyclic quadrilaterals
Circle geometry
Circle geometryMathletics Instant Workbooks – Series K 2 Copyright © 3P Learning 5
71Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)UNIT 5: The angle in the alternate segment
EXCEL YEARS 9 & 10 ADVANCED MATHS
Page 219
QUESTION 1 Find the value of the pronumeral.
a b c
______________________ ______________________ ______________________
______________________ ______________________ ______________________
d e f
______________________ ______________________ ______________________
______________________ ______________________ ______________________
QUESTION 2 Find the value of the pronumeral.
a b c
______________________ ______________________ ______________________
______________________ ______________________ ______________________
d e f
______________________ ______________________ ______________________
______________________ ______________________ ______________________
m°
50°
T
A
B
Pa°
45° T
A
B
P
x°
30°
T
A
B
P
x°
48°
T
A
B
Py°
60°n°
35°
m°
70°p°
y° 50°
x°
70°
y° 20°
x°
135°
b°
50°
a°
65°c°
y° 70°
x°
80°
a° 75°
b° 80°
a°
55°
b°
n°
40°m°
Topic 5 - The angle in the alternate segment
Circle geometry
Circle geometryMathletics Instant Workbooks – Series K 2 Copyright © 3P Learning 6
72 EXCEL ESSENTIAL SKILLS: YEAR 10 MATHS REVISION AND EXAM WORKBOOK 2 – EXTENSION
Circle geometry (OPTION 5)
QUESTION 2 Find the value of the pronumeral. All measurements are in centimetres.
a b
_____________________________________ _____________________________________
_____________________________________ _____________________________________
c d
_____________________________________ _____________________________________
_____________________________________ _____________________________________
UNIT 6: Further properties of a circle
EXCEL YEARS 9 & 10 ADVANCED MATHS
Page 218
QUESTION 1 Find the value of the pronumeral. All measurements are in centimetres.
a b
______________________ ______________________
______________________ ______________________
______________________ ______________________
c d
______________________ ______________________
______________________ ______________________
______________________ ______________________
3
x 10
15
C
A D
B
E
16a
20
4C
A
D
BE
8
y
8
2
C
A
D
B
E
2
x5
4
C
A
D
BE
12
m8
6
C
A
D
B
E
3
y
9 2
C
A D
BE
3a
7
7
C
A
D
BE
QUESTION 3 Find the value of the pronumeral. All measurements are in centimetres.
a b
_____________________________________ _____________________________________
_____________________________________ _____________________________________
4
x
5
R
Q
PT
21
a
4RQ
P
T
6
m
2
8
C
A
D
BE
Topic 6 - Further properties of a circle
Circle geometry
Circle geometryMathletics Instant Workbooks – Series K 2 Copyright © 3P Learning 7
Topic 7 - Deductive exercises related to the circle
73Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)UNIT 7: Deductive exercises related to the circle
EXCEL YEARS 9 & 10 ADVANCED MATHS
Pages 220–222
QUESTION 1 Find the value of the pronumeral.
a b
_____________________________________ _____________________________________
_____________________________________ _____________________________________
_____________________________________ _____________________________________
c d
_____________________________________ _____________________________________
_____________________________________ _____________________________________
_____________________________________ _____________________________________
a°
50°
x°40°
O
C
A
B D
a°70°
O
C
Q
R
Pb°
QUESTION 2 Find the value of the pronumeral.
a b
_____________________________________ _____________________________________
_____________________________________ _____________________________________
_____________________________________ _____________________________________
c d
_____________________________________ _____________________________________
_____________________________________ _____________________________________
_____________________________________ _____________________________________
46°
D
C
B
A55°
m°
C
BA 60°x° y°
O
55°
x°
y°
a°
38°
O
C
A
B
75°
68°a°
b°
c°
Circle geometry
Circle geometryMathletics Instant Workbooks – Series K 2 Copyright © 3P Learning 8
Topic 8 - Miscellaneous questions
74 EXCEL ESSENTIAL SKILLS: YEAR 10 MATHS REVISION AND EXAM WORKBOOK 2 – EXTENSION
Circle geometry (OPTION 5)UNIT 8: Miscellaneous questions
EXCEL YEARS 9 & 10 ADVANCED MATHS
Page 224
QUESTION 1 Find the value of the pronumeral.
a b c
______________________ ______________________ ______________________
QUESTION 2 Find the value of the pronumeral.
a b c
______________________ ______________________ ______________________
QUESTION 3 Find the value of the pronumeral.
a b c
______________________ ______________________ ______________________
QUESTION 4 Find the value of the pronumeral.
a b c
______________________ ______________________ ______________________
QUESTION 5 Find the value of the pronumeral.
a b c
______________________ ______________________ ______________________
xA B
O
M
AB = 16 cm
a°A B
O
M
AM = BM = 12 cm
x°
A
B
O
C
D
85°
C
m°
96°
AB
O
a° 50°b°
O
a°P T
O
y°70°T
x cm
9 cmQ
P
m°110°
n°
65°
y°
110°x°
m°
95° n°
x°
75°
y°
30°
4
x 12
164
x
5
3
x°
O
75Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)
TOPIC TEST SECTION 1
Instructions for SECTION 1 • You have 15 minutes to answer Section 1• Each question is worth 1 mark• Attempt ALL questions• Calculators are NOT to be used• Fill in only ONE CIRCLE for each question
1 The distance around a circle is called the
A diameter B circumference C radius D secant
2 The angle in a semicircle is equal to
A 45° B 90° C 180° D 270°
3 The opposite angles of a cyclic quadrilateral add up to
A 90° B 180° C 270° D 360°
4 The angle between the tangent and the radius through the point of contact is
A 45° B 90° C 135° D 170°
5 The number of diameters a circle has, equals
A 1 B 2 C 3 D infinite
6 The axis of symmetry of a circle is called a
A chord B radius C diameter D tangent
7 The maximum number of points in which a straight line can cut a circle are
A 1 B 2 C 3 D 4
8 Circles of different radii which have a common centre are called
A semicircles B cyclics C concentric D none of these
9 A straight line that touches a circle at one point only is called the
A radius B diameter C tangent D secant
10 The tangents at the ends of any diameter are
A perpendicular B parallel C bisect D none of these
Marks
Total marks achieved for SECTION 110
1
1
1
1
1
1
1
1
1
1
Circle geometry (OPTION 5)
75Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)
TOPIC TEST SECTION 1
Instructions for SECTION 1 • You have 15 minutes to answer Section 1• Each question is worth 1 mark• Attempt ALL questions• Calculators are NOT to be used• Fill in only ONE CIRCLE for each question
1 The distance around a circle is called the
A diameter B circumference C radius D secant
2 The angle in a semicircle is equal to
A 45° B 90° C 180° D 270°
3 The opposite angles of a cyclic quadrilateral add up to
A 90° B 180° C 270° D 360°
4 The angle between the tangent and the radius through the point of contact is
A 45° B 90° C 135° D 170°
5 The number of diameters a circle has, equals
A 1 B 2 C 3 D infinite
6 The axis of symmetry of a circle is called a
A chord B radius C diameter D tangent
7 The maximum number of points in which a straight line can cut a circle are
A 1 B 2 C 3 D 4
8 Circles of different radii which have a common centre are called
A semicircles B cyclics C concentric D none of these
9 A straight line that touches a circle at one point only is called the
A radius B diameter C tangent D secant
10 The tangents at the ends of any diameter are
A perpendicular B parallel C bisect D none of these
Marks
Total marks achieved for SECTION 110
1
1
1
1
1
1
1
1
1
1
Circle geometry (OPTION 5)
Circle geometryMathletics Instant Workbooks – Series K 2 Copyright © 3P Learning 9
Circle geometryTopic Test PART A
Marks
Total marks achieved for PART A 10
Instructions 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
Total marks achieved for PART B 15
Marks
Circle geometryTopic Test PART B
Circle geometryMathletics Instant Workbooks – Series K 2 Copyright © 3P Learning 10
Instructions This part consists of 15 questions Each question is worth 1 mark Attempt ALL questions Calculators may be usedTime allowed: 20 minutes Total marks = 15
Questions Answers only
76 EXCEL ESSENTIAL SKILLS: YEAR 10 MATHS REVISION AND EXAM WORKBOOK 2 – EXTENSION
Circle geometry (OPTION 5)
TOPIC TEST SECTION 2
Instructions for SECTION 2 • You have 20 minutes to answer ALL of Section 2• Each question is worth 2 marks• Attempt ALL questions• Calculators may be used
Marks
Total marks achieved for SECTION 230
A circle has centre O and COD is a straight line.
1 Find the size of the obtuse angle AOB. ___________________
2 What is the size of ∠DAC? ___________________
Complete the following sentences.
3 Equal chords are . . . . . . . . from the centre. ___________________
4 Equal chords make . . . . . . . . angles at the centre. ___________________
5 A line from the centre of a circle, perpendicular to a chord,. . . . . . . the chord. ___________________
6 The right bisector of any chord of a circle passes throughthe . . . . . . . . ___________________
7 The angle at the centre of a circle is . . . . . . . . the angle at thecircumference standing on the same arc. ___________________
8 The angle in a semicircle is a . . . . . . . . ___________________
9 Angles in the same segment of a circle are . . . . . . . . ___________________
10 The opposite angles of a cyclic quadrilateral are . . . . . . . . ___________________
11 The angle between a tangent and the radius throughits point of contact is always equal to . . . . . . . . ___________________
12 The tangents drawn to a circle from an externalpoint are . . . . . . . . in length. ___________________
13 The tangents at the end of any diameter are . . . . . . . . ___________________
14 The line from the centre of a circle to the midpoint of achord meets the chord at . . . . . . . . angles. ___________________
15 When two circles intersect, the line joining their centresbisects the common chord at . . . . . . . . angles. ___________________
Questions Answers
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
A
B
O
C
D
60°
Circle geometry (OPTION 5)
76 EXCEL ESSENTIAL SKILLS: YEAR 10 MATHS REVISION AND EXAM WORKBOOK 2 – EXTENSION
Circle geometry (OPTION 5)
TOPIC TEST SECTION 2
Instructions for SECTION 2 • You have 20 minutes to answer ALL of Section 2• Each question is worth 2 marks• Attempt ALL questions• Calculators may be used
Marks
Total marks achieved for SECTION 230
A circle has centre O and COD is a straight line.
1 Find the size of the obtuse angle AOB. ___________________
2 What is the size of ∠DAC? ___________________
Complete the following sentences.
3 Equal chords are . . . . . . . . from the centre. ___________________
4 Equal chords make . . . . . . . . angles at the centre. ___________________
5 A line from the centre of a circle, perpendicular to a chord,. . . . . . . the chord. ___________________
6 The right bisector of any chord of a circle passes throughthe . . . . . . . . ___________________
7 The angle at the centre of a circle is . . . . . . . . the angle at thecircumference standing on the same arc. ___________________
8 The angle in a semicircle is a . . . . . . . . ___________________
9 Angles in the same segment of a circle are . . . . . . . . ___________________
10 The opposite angles of a cyclic quadrilateral are . . . . . . . . ___________________
11 The angle between a tangent and the radius throughits point of contact is always equal to . . . . . . . . ___________________
12 The tangents drawn to a circle from an externalpoint are . . . . . . . . in length. ___________________
13 The tangents at the end of any diameter are . . . . . . . . ___________________
14 The line from the centre of a circle to the midpoint of achord meets the chord at . . . . . . . . angles. ___________________
15 When two circles intersect, the line joining their centresbisects the common chord at . . . . . . . . angles. ___________________
Questions Answers
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
A
B
O
C
D
60°
Circle geometry (OPTION 5)
75Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)
TOPIC TEST SECTION 1
Instructions for SECTION 1 • You have 15 minutes to answer Section 1• Each question is worth 1 mark• Attempt ALL questions• Calculators are NOT to be used• Fill in only ONE CIRCLE for each question
1 The distance around a circle is called the
A diameter B circumference C radius D secant
2 The angle in a semicircle is equal to
A 45° B 90° C 180° D 270°
3 The opposite angles of a cyclic quadrilateral add up to
A 90° B 180° C 270° D 360°
4 The angle between the tangent and the radius through the point of contact is
A 45° B 90° C 135° D 170°
5 The number of diameters a circle has, equals
A 1 B 2 C 3 D infinite
6 The axis of symmetry of a circle is called a
A chord B radius C diameter D tangent
7 The maximum number of points in which a straight line can cut a circle are
A 1 B 2 C 3 D 4
8 Circles of different radii which have a common centre are called
A semicircles B cyclics C concentric D none of these
9 A straight line that touches a circle at one point only is called the
A radius B diameter C tangent D secant
10 The tangents at the ends of any diameter are
A perpendicular B parallel C bisect D none of these
Marks
Total marks achieved for SECTION 110
1
1
1
1
1
1
1
1
1
1
Circle geometry (OPTION 5)
75Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)
TOPIC TEST SECTION 1
Instructions for SECTION 1 • You have 15 minutes to answer Section 1• Each question is worth 1 mark• Attempt ALL questions• Calculators are NOT to be used• Fill in only ONE CIRCLE for each question
1 The distance around a circle is called the
A diameter B circumference C radius D secant
2 The angle in a semicircle is equal to
A 45° B 90° C 180° D 270°
3 The opposite angles of a cyclic quadrilateral add up to
A 90° B 180° C 270° D 360°
4 The angle between the tangent and the radius through the point of contact is
A 45° B 90° C 135° D 170°
5 The number of diameters a circle has, equals
A 1 B 2 C 3 D infinite
6 The axis of symmetry of a circle is called a
A chord B radius C diameter D tangent
7 The maximum number of points in which a straight line can cut a circle are
A 1 B 2 C 3 D 4
8 Circles of different radii which have a common centre are called
A semicircles B cyclics C concentric D none of these
9 A straight line that touches a circle at one point only is called the
A radius B diameter C tangent D secant
10 The tangents at the ends of any diameter are
A perpendicular B parallel C bisect D none of these
Marks
Total marks achieved for SECTION 110
1
1
1
1
1
1
1
1
1
1
Circle geometry (OPTION 5)
75Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)
TOPIC TEST SECTION 1
Instructions for SECTION 1 • You have 15 minutes to answer Section 1• Each question is worth 1 mark• Attempt ALL questions• Calculators are NOT to be used• Fill in only ONE CIRCLE for each question
1 The distance around a circle is called the
A diameter B circumference C radius D secant
2 The angle in a semicircle is equal to
A 45° B 90° C 180° D 270°
3 The opposite angles of a cyclic quadrilateral add up to
A 90° B 180° C 270° D 360°
4 The angle between the tangent and the radius through the point of contact is
A 45° B 90° C 135° D 170°
5 The number of diameters a circle has, equals
A 1 B 2 C 3 D infinite
6 The axis of symmetry of a circle is called a
A chord B radius C diameter D tangent
7 The maximum number of points in which a straight line can cut a circle are
A 1 B 2 C 3 D 4
8 Circles of different radii which have a common centre are called
A semicircles B cyclics C concentric D none of these
9 A straight line that touches a circle at one point only is called the
A radius B diameter C tangent D secant
10 The tangents at the ends of any diameter are
A perpendicular B parallel C bisect D none of these
Marks
Total marks achieved for SECTION 110
1
1
1
1
1
1
1
1
1
1
Circle geometry (OPTION 5)
75Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)
TOPIC TEST SECTION 1
Instructions for SECTION 1 • You have 15 minutes to answer Section 1• Each question is worth 1 mark• Attempt ALL questions• Calculators are NOT to be used• Fill in only ONE CIRCLE for each question
1 The distance around a circle is called the
A diameter B circumference C radius D secant
2 The angle in a semicircle is equal to
A 45° B 90° C 180° D 270°
3 The opposite angles of a cyclic quadrilateral add up to
A 90° B 180° C 270° D 360°
4 The angle between the tangent and the radius through the point of contact is
A 45° B 90° C 135° D 170°
5 The number of diameters a circle has, equals
A 1 B 2 C 3 D infinite
6 The axis of symmetry of a circle is called a
A chord B radius C diameter D tangent
7 The maximum number of points in which a straight line can cut a circle are
A 1 B 2 C 3 D 4
8 Circles of different radii which have a common centre are called
A semicircles B cyclics C concentric D none of these
9 A straight line that touches a circle at one point only is called the
A radius B diameter C tangent D secant
10 The tangents at the ends of any diameter are
A perpendicular B parallel C bisect D none of these
Marks
Total marks achieved for SECTION 110
1
1
1
1
1
1
1
1
1
1
Circle geometry (OPTION 5)
75Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)
TOPIC TEST SECTION 1
Instructions for SECTION 1 • You have 15 minutes to answer Section 1• Each question is worth 1 mark• Attempt ALL questions• Calculators are NOT to be used• Fill in only ONE CIRCLE for each question
1 The distance around a circle is called the
A diameter B circumference C radius D secant
2 The angle in a semicircle is equal to
A 45° B 90° C 180° D 270°
3 The opposite angles of a cyclic quadrilateral add up to
A 90° B 180° C 270° D 360°
4 The angle between the tangent and the radius through the point of contact is
A 45° B 90° C 135° D 170°
5 The number of diameters a circle has, equals
A 1 B 2 C 3 D infinite
6 The axis of symmetry of a circle is called a
A chord B radius C diameter D tangent
7 The maximum number of points in which a straight line can cut a circle are
A 1 B 2 C 3 D 4
8 Circles of different radii which have a common centre are called
A semicircles B cyclics C concentric D none of these
9 A straight line that touches a circle at one point only is called the
A radius B diameter C tangent D secant
10 The tangents at the ends of any diameter are
A perpendicular B parallel C bisect D none of these
Marks
Total marks achieved for SECTION 110
1
1
1
1
1
1
1
1
1
1
Circle geometry (OPTION 5)
75Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)
TOPIC TEST SECTION 1
Instructions for SECTION 1 • You have 15 minutes to answer Section 1• Each question is worth 1 mark• Attempt ALL questions• Calculators are NOT to be used• Fill in only ONE CIRCLE for each question
1 The distance around a circle is called the
A diameter B circumference C radius D secant
2 The angle in a semicircle is equal to
A 45° B 90° C 180° D 270°
3 The opposite angles of a cyclic quadrilateral add up to
A 90° B 180° C 270° D 360°
4 The angle between the tangent and the radius through the point of contact is
A 45° B 90° C 135° D 170°
5 The number of diameters a circle has, equals
A 1 B 2 C 3 D infinite
6 The axis of symmetry of a circle is called a
A chord B radius C diameter D tangent
7 The maximum number of points in which a straight line can cut a circle are
A 1 B 2 C 3 D 4
8 Circles of different radii which have a common centre are called
A semicircles B cyclics C concentric D none of these
9 A straight line that touches a circle at one point only is called the
A radius B diameter C tangent D secant
10 The tangents at the ends of any diameter are
A perpendicular B parallel C bisect D none of these
Marks
Total marks achieved for SECTION 110
1
1
1
1
1
1
1
1
1
1
Circle geometry (OPTION 5)
75Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)
TOPIC TEST SECTION 1
Instructions for SECTION 1 • You have 15 minutes to answer Section 1• Each question is worth 1 mark• Attempt ALL questions• Calculators are NOT to be used• Fill in only ONE CIRCLE for each question
1 The distance around a circle is called the
A diameter B circumference C radius D secant
2 The angle in a semicircle is equal to
A 45° B 90° C 180° D 270°
3 The opposite angles of a cyclic quadrilateral add up to
A 90° B 180° C 270° D 360°
4 The angle between the tangent and the radius through the point of contact is
A 45° B 90° C 135° D 170°
5 The number of diameters a circle has, equals
A 1 B 2 C 3 D infinite
6 The axis of symmetry of a circle is called a
A chord B radius C diameter D tangent
7 The maximum number of points in which a straight line can cut a circle are
A 1 B 2 C 3 D 4
8 Circles of different radii which have a common centre are called
A semicircles B cyclics C concentric D none of these
9 A straight line that touches a circle at one point only is called the
A radius B diameter C tangent D secant
10 The tangents at the ends of any diameter are
A perpendicular B parallel C bisect D none of these
Marks
Total marks achieved for SECTION 110
1
1
1
1
1
1
1
1
1
1
Circle geometry (OPTION 5)
75Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)
TOPIC TEST SECTION 1
Instructions for SECTION 1 • You have 15 minutes to answer Section 1• Each question is worth 1 mark• Attempt ALL questions• Calculators are NOT to be used• Fill in only ONE CIRCLE for each question
1 The distance around a circle is called the
A diameter B circumference C radius D secant
2 The angle in a semicircle is equal to
A 45° B 90° C 180° D 270°
3 The opposite angles of a cyclic quadrilateral add up to
A 90° B 180° C 270° D 360°
4 The angle between the tangent and the radius through the point of contact is
A 45° B 90° C 135° D 170°
5 The number of diameters a circle has, equals
A 1 B 2 C 3 D infinite
6 The axis of symmetry of a circle is called a
A chord B radius C diameter D tangent
7 The maximum number of points in which a straight line can cut a circle are
A 1 B 2 C 3 D 4
8 Circles of different radii which have a common centre are called
A semicircles B cyclics C concentric D none of these
9 A straight line that touches a circle at one point only is called the
A radius B diameter C tangent D secant
10 The tangents at the ends of any diameter are
A perpendicular B parallel C bisect D none of these
Marks
Total marks achieved for SECTION 110
1
1
1
1
1
1
1
1
1
1
Circle geometry (OPTION 5)
75Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)
TOPIC TEST SECTION 1
Instructions for SECTION 1 • You have 15 minutes to answer Section 1• Each question is worth 1 mark• Attempt ALL questions• Calculators are NOT to be used• Fill in only ONE CIRCLE for each question
1 The distance around a circle is called the
A diameter B circumference C radius D secant
2 The angle in a semicircle is equal to
A 45° B 90° C 180° D 270°
3 The opposite angles of a cyclic quadrilateral add up to
A 90° B 180° C 270° D 360°
4 The angle between the tangent and the radius through the point of contact is
A 45° B 90° C 135° D 170°
5 The number of diameters a circle has, equals
A 1 B 2 C 3 D infinite
6 The axis of symmetry of a circle is called a
A chord B radius C diameter D tangent
7 The maximum number of points in which a straight line can cut a circle are
A 1 B 2 C 3 D 4
8 Circles of different radii which have a common centre are called
A semicircles B cyclics C concentric D none of these
9 A straight line that touches a circle at one point only is called the
A radius B diameter C tangent D secant
10 The tangents at the ends of any diameter are
A perpendicular B parallel C bisect D none of these
Marks
Total marks achieved for SECTION 110
1
1
1
1
1
1
1
1
1
1
Circle geometry (OPTION 5)
75Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)
TOPIC TEST SECTION 1
Instructions for SECTION 1 • You have 15 minutes to answer Section 1• Each question is worth 1 mark• Attempt ALL questions• Calculators are NOT to be used• Fill in only ONE CIRCLE for each question
1 The distance around a circle is called the
A diameter B circumference C radius D secant
2 The angle in a semicircle is equal to
A 45° B 90° C 180° D 270°
3 The opposite angles of a cyclic quadrilateral add up to
A 90° B 180° C 270° D 360°
4 The angle between the tangent and the radius through the point of contact is
A 45° B 90° C 135° D 170°
5 The number of diameters a circle has, equals
A 1 B 2 C 3 D infinite
6 The axis of symmetry of a circle is called a
A chord B radius C diameter D tangent
7 The maximum number of points in which a straight line can cut a circle are
A 1 B 2 C 3 D 4
8 Circles of different radii which have a common centre are called
A semicircles B cyclics C concentric D none of these
9 A straight line that touches a circle at one point only is called the
A radius B diameter C tangent D secant
10 The tangents at the ends of any diameter are
A perpendicular B parallel C bisect D none of these
Marks
Total marks achieved for SECTION 110
1
1
1
1
1
1
1
1
1
1
Circle geometry (OPTION 5)
75Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)
TOPIC TEST SECTION 1
Instructions for SECTION 1 • You have 15 minutes to answer Section 1• Each question is worth 1 mark• Attempt ALL questions• Calculators are NOT to be used• Fill in only ONE CIRCLE for each question
1 The distance around a circle is called the
A diameter B circumference C radius D secant
2 The angle in a semicircle is equal to
A 45° B 90° C 180° D 270°
3 The opposite angles of a cyclic quadrilateral add up to
A 90° B 180° C 270° D 360°
4 The angle between the tangent and the radius through the point of contact is
A 45° B 90° C 135° D 170°
5 The number of diameters a circle has, equals
A 1 B 2 C 3 D infinite
6 The axis of symmetry of a circle is called a
A chord B radius C diameter D tangent
7 The maximum number of points in which a straight line can cut a circle are
A 1 B 2 C 3 D 4
8 Circles of different radii which have a common centre are called
A semicircles B cyclics C concentric D none of these
9 A straight line that touches a circle at one point only is called the
A radius B diameter C tangent D secant
10 The tangents at the ends of any diameter are
A perpendicular B parallel C bisect D none of these
Marks
Total marks achieved for SECTION 110
1
1
1
1
1
1
1
1
1
1
Circle geometry (OPTION 5)
75Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)
TOPIC TEST SECTION 1
Instructions for SECTION 1 • You have 15 minutes to answer Section 1• Each question is worth 1 mark• Attempt ALL questions• Calculators are NOT to be used• Fill in only ONE CIRCLE for each question
1 The distance around a circle is called the
A diameter B circumference C radius D secant
2 The angle in a semicircle is equal to
A 45° B 90° C 180° D 270°
3 The opposite angles of a cyclic quadrilateral add up to
A 90° B 180° C 270° D 360°
4 The angle between the tangent and the radius through the point of contact is
A 45° B 90° C 135° D 170°
5 The number of diameters a circle has, equals
A 1 B 2 C 3 D infinite
6 The axis of symmetry of a circle is called a
A chord B radius C diameter D tangent
7 The maximum number of points in which a straight line can cut a circle are
A 1 B 2 C 3 D 4
8 Circles of different radii which have a common centre are called
A semicircles B cyclics C concentric D none of these
9 A straight line that touches a circle at one point only is called the
A radius B diameter C tangent D secant
10 The tangents at the ends of any diameter are
A perpendicular B parallel C bisect D none of these
Marks
Total marks achieved for SECTION 110
1
1
1
1
1
1
1
1
1
1
Circle geometry (OPTION 5)
75Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)
TOPIC TEST SECTION 1
Instructions for SECTION 1 • You have 15 minutes to answer Section 1• Each question is worth 1 mark• Attempt ALL questions• Calculators are NOT to be used• Fill in only ONE CIRCLE for each question
1 The distance around a circle is called the
A diameter B circumference C radius D secant
2 The angle in a semicircle is equal to
A 45° B 90° C 180° D 270°
3 The opposite angles of a cyclic quadrilateral add up to
A 90° B 180° C 270° D 360°
4 The angle between the tangent and the radius through the point of contact is
A 45° B 90° C 135° D 170°
5 The number of diameters a circle has, equals
A 1 B 2 C 3 D infinite
6 The axis of symmetry of a circle is called a
A chord B radius C diameter D tangent
7 The maximum number of points in which a straight line can cut a circle are
A 1 B 2 C 3 D 4
8 Circles of different radii which have a common centre are called
A semicircles B cyclics C concentric D none of these
9 A straight line that touches a circle at one point only is called the
A radius B diameter C tangent D secant
10 The tangents at the ends of any diameter are
A perpendicular B parallel C bisect D none of these
Marks
Total marks achieved for SECTION 110
1
1
1
1
1
1
1
1
1
1
Circle geometry (OPTION 5)
75Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)
TOPIC TEST SECTION 1
Instructions for SECTION 1 • You have 15 minutes to answer Section 1• Each question is worth 1 mark• Attempt ALL questions• Calculators are NOT to be used• Fill in only ONE CIRCLE for each question
1 The distance around a circle is called the
A diameter B circumference C radius D secant
2 The angle in a semicircle is equal to
A 45° B 90° C 180° D 270°
3 The opposite angles of a cyclic quadrilateral add up to
A 90° B 180° C 270° D 360°
4 The angle between the tangent and the radius through the point of contact is
A 45° B 90° C 135° D 170°
5 The number of diameters a circle has, equals
A 1 B 2 C 3 D infinite
6 The axis of symmetry of a circle is called a
A chord B radius C diameter D tangent
7 The maximum number of points in which a straight line can cut a circle are
A 1 B 2 C 3 D 4
8 Circles of different radii which have a common centre are called
A semicircles B cyclics C concentric D none of these
9 A straight line that touches a circle at one point only is called the
A radius B diameter C tangent D secant
10 The tangents at the ends of any diameter are
A perpendicular B parallel C bisect D none of these
Marks
Total marks achieved for SECTION 110
1
1
1
1
1
1
1
1
1
1
Circle geometry (OPTION 5)
75Chapter 8: Circle geometry (Option 5)
Circle geometry (OPTION 5)
TOPIC TEST SECTION 1
Instructions for SECTION 1 • You have 15 minutes to answer Section 1• Each question is worth 1 mark• Attempt ALL questions• Calculators are NOT to be used• Fill in only ONE CIRCLE for each question
1 The distance around a circle is called the
A diameter B circumference C radius D secant
2 The angle in a semicircle is equal to
A 45° B 90° C 180° D 270°
3 The opposite angles of a cyclic quadrilateral add up to
A 90° B 180° C 270° D 360°
4 The angle between the tangent and the radius through the point of contact is
A 45° B 90° C 135° D 170°
5 The number of diameters a circle has, equals
A 1 B 2 C 3 D infinite
6 The axis of symmetry of a circle is called a
A chord B radius C diameter D tangent
7 The maximum number of points in which a straight line can cut a circle are
A 1 B 2 C 3 D 4
8 Circles of different radii which have a common centre are called
A semicircles B cyclics C concentric D none of these
9 A straight line that touches a circle at one point only is called the
A radius B diameter C tangent D secant
10 The tangents at the ends of any diameter are
A perpendicular B parallel C bisect D none of these
Marks
Total marks achieved for SECTION 110
1
1
1
1
1
1
1
1
1
1
Circle geometry (OPTION 5)