1. ppr maths nbk
CHAPTER 8 : CIRCLES III
EXERCISE 1
1. Given PQR is a tangent to the circle QSTU.
T
Find the value of
y˚ a) x
S U
35˚
b) y
x˚
P Q R
Answer: a)………………..
b)………………..
2. In the diagram, ABC is a tangent to the circle BEFG.
E
Find the value of
A y˚ 40˚ 110˚ F a) x
x˚
B G
b) y
C Answer: a)………………..
b)………………..
3. PQR is a tangent to the circle QSTU with centre O.
Find the value of
T a) x
y˚ U
O•
S x˚ R b) y
40˚
30˚ Q
P Answer: a)………………..
b)………………..
4. In the diagram, PQR is a tangent to the circle with centre O.
Find the value of
35˚ a) x
•
·
O
60˚
x˚ y˚
P b) y Answer : a)……………………..
Q R b)…………………….
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5. In the diagram, ABC is a tangent to the circle with centre O.
Find the value of
a) p
q˚
34˚ O•
p˚ b) q
80˚ C
B
A
Answer: a)………………..
b)………………..
6. In the diagram, FGH is a tangent to the circle centre O, at point G. Find the value of y.
E
100˚
D
O y˚
F 40˚
G
H
Answer: …………………
7. In the diagram, PQR is a tangent to the circle centre O, at point Q. Find the value of
y.
35˚ O
P y˚
42˚
Q
R
Answer: .…………………
8. In the diagram below, PQR is a tangent to the circle centre O, at point Q. PTOS is a
straight line. Find the value of y.
T O S
P 42˚
y˚
Q
R Answer: ..…………………
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9. In the diagram below, PQR is a tangent to the circle centre O, at point Q. Find the
value of y.
T
P
S 26˚
y˚ Q
R
Answer: a)…………………
10. In the diagram, EFG is a tangent to the circle FLMN. Find the value of y.
M
105˚
L 35˚ G
y˚
F
E
Answer: a)…………………
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CHAPTER 8 : CIRCLES III
EXERCISE 2
1. In the diagram, DEFG is a tangent to the circle with centre O. EOJ, FKJ and GKOH
are straight lines. Find the value of
J a) p
H
p˚
30˚ • O
· b) q
K
q˚ r˚
D E F G c) r
Answer: a)………………..
b)……………….
c)………………..
2. In the diagram, ABC is a tangent to the circle with centre O. EODC is a straight line.
F Find the value of
p˚ a) p
E
O
• r˚ b) q
48˚ D C
q˚ c) r
A B
Answer: a)………………..
b)……………….
c)………………..
3. In the diagram, PQ is a tangent to the circle with centre O. POR and SOQ are straight
lines. S Find the value of
a) x
R
O• y˚ b) y
x˚
24˚ z˚ c) z
P Q
Answer: a)………………..
b)……………….
c)………………..
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4. In the diagram, PTQ is a tangent to the circle to the circle with centre O. PAB is a
straight line.
Find the value of
B a) x
x˚
O• z˚ b) y
80˚ A
y˚ 30˚ c) z
Q T P
Answer: a)………………..
b)……………….
c)………………..
5. In the diagram, VST is a tangent to the circle with centre O. PORV, TOQ and QRS are
straight lines.
Find the value of
Q a) x
P
34˚ •O b) y
R
x˚ y˚
T S V
Answer: a)………………..
b)……………….
6. In the diagram below, PQR is a tangent to the circle at point Q. The centre of the
circle is O. Find the value of x.
75
X
o
Answer: .…………………
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7. In the diagram below, PQR is a tangent to the circle at point Q. TOQ is the diameter
of the circle and O is the centre of the circle. Find the value of x.
xo
34
Answer: …………………
8. In the diagram below, EFG is a tangent to the circle centre O, at point F. Find the
value of x.
62 o
Answer:……………………
9. In the diagram below, PQ and RS are common tangents to the circles centres O and T,
at P, R, Q and S respectively. Find the value of x.
150o xo
Answer:……………………….
10 In the diagram , EF is a common tangent to the circles centres O and Q, at points E
and F respectively. OHQ is a straight line. Find the value of x.
25˚
25 o Answer: …………………
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CHAPTER 8 : CIRCLES III
DIAGNOSTIC TEST
1. In the diagram, tangent PQ touches the circle at Q. Find the value of x.
T A 30 o
B 70 o
C 80 o
P 30˚ D 100 o
100˚ S
x˚
Q R
2. In the diagram, PQ is a tangent to the circle with centre O at P. Find the value of y.
S
A 40 o
y˚ B 50 o
O• 120˚ R C 60 o
D 70 o
40˚ Q
P
3. In the diagram, PQ is a tangent to the circle at Q. Find the value of x.
Q
P A 30 o
50˚ x˚
B 40 o
T 80˚ R C 50 o
D 80 o
S
4. In the diagram, PQR is a tangent to the circle with centre O at Q. Find the value of y.
A 40 o
S
B 50 o
T 65˚ 100˚ C 65 o
O
D 115 o
y˚
P Q R
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5. In the diagram, RS is a tangent to the circle at S and PQR is a straight line. Find the
value of x.
A 20˚
P B 25 o
C 30 o
D 40 o
Q
40˚ x˚
S R
6. In the diagram below, EFG and HFJ are common tangents to the circles centre O and
Q, at J, G, E and H respectively. Find the value of x.
A. 76˚
B. 52˚
C. 104˚
D. 90˚
xo
7. In the diagram below, LMN is a tangent to the circle at M. POQ is the diameter of
the circle. Find the value of y.
A. 42˚
B. 132˚
C. 138˚
D. 48˚
42˚
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8. In the diagram below, LMN is a tangent to the circle centre O, at the point M. LQOP
is a straight line. Find the value of x.
A. 65˚
B. 15˚
C. 50˚
D. 40˚
25
9. In the diagram below, shows two circle with a common tangent PQR at point Q.
MNQ is a straight line. What is the value of x?
A. 100˚
B. 80˚
C. 115˚
55o
D. 65˚
45o
10. In the diagram below, PQ and PR are tangents to the circle at Q and R respectively.
O is the centre of the circle. Find the value of y
A. 84 o
42o B. 48 o
C. 96 o
yo D. 42 o
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