Chapter 3 - Circles II
Transcript of Chapter 3 - Circles II
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