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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 b) y P Q R Answer a)helliphelliphelliphelliphelliphellip

b)helliphelliphelliphelliphelliphellip 2 In the diagram ABC is a tangent to the circle BEFG E Find the value of A F a) x B G b) y C Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip 3 PQR is a tangent to the circle QSTU with centre O Find the value of T a) x U O S R b) y Q P Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip 4 In the diagram PQR is a tangent to the circle with centre O Find the value of a) x O P b) y Answer a)helliphelliphelliphelliphelliphelliphelliphellip Q R b)helliphelliphelliphelliphelliphelliphelliphellip

x˚

35˚

y˚ x˚

40˚ 110˚

x˚ y˚

40˚ 30˚

y˚ x˚

35˚

60˚ bull

bull

ppr maths nbk

86

5 In the diagram ABC is a tangent to the circle with centre O Find the value of a) p O b) q C B A Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip 6 In the diagram FGH is a tangent to the circle centre O at point G Find the value of y D F G H Answer helliphelliphelliphelliphelliphelliphellip 7 In the diagram PQR is a tangent to the circle centre O at point Q Find the value of

y P Q R Answer helliphelliphelliphelliphelliphelliphellip 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 S P Q R Answer helliphelliphelliphelliphelliphelliphellip

80˚

34˚ bull

p˚

q˚

100˚

40˚ y˚

E

O

y˚ O 35˚

42˚

y˚ 42˚ O

ppr maths nbk

87

9 In the diagram below PQR is a tangent to the circle centre O at point Q Find the

value of y P S Q R Answer a)helliphelliphelliphelliphelliphelliphellip 10 In the diagram EFG is a tangent to the circle FLMN Find the value of y M L G F E Answer a)helliphelliphelliphelliphelliphelliphellip

26˚ y˚

T

y˚

105˚ 35˚

ppr maths nbk

88

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 O b) q K D E F G c) r Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip c)helliphelliphelliphelliphelliphellip 2 In the diagram ABC is a tangent to the circle with centre O EODC is a straight line F Find the value of a) p E b) q D C c) r A B Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip c)helliphelliphelliphelliphelliphellip 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 b) y c) z

Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip c)helliphelliphelliphelliphelliphellip

30˚ p˚

q˚ r˚

Op˚

q˚

r˚ 48˚

bull

bull

Q P

bullx˚

y˚

z˚ 24˚

ppr maths nbk

89

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 O b) y A c) z Q T P Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip c)helliphelliphelliphelliphelliphellip 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 b) y R T S V Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip 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 Answer helliphelliphelliphelliphelliphelliphellip

x˚

y˚

z˚ 80˚

30˚

bull

O bull

x˚ y˚

34˚

75

Xo

ppr maths nbk

90

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 Answer helliphelliphelliphelliphelliphelliphellip 8 In the diagram below EFG is a tangent to the circle centre O at point F Find the value of x Answerhelliphelliphelliphelliphelliphelliphelliphellip 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 Answerhelliphelliphelliphelliphelliphelliphelliphelliphellip 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 Answer helliphelliphelliphelliphelliphelliphellip

34

xo

25 o

62 o

xo150o

25˚

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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 S D 100 o Q R 2 In the diagram PQ is a tangent to the circle with centre O at P Find the value of y A 40 o B 50 o C 60 o D 70 o 3 In the diagram PQ is a tangent to the circle at Q Find the value of x A 30 o B 40 o C 50 o D 80 o 4 In the diagram PQR is a tangent to the circle with centre O at Q Find the value of y A 40 o B 50 o C 65 o D 115 o

x˚ 100˚ 30˚

O bull

y˚

120˚

40˚ P

Q

S

R

PQ

R

S

T 80˚

x˚ 50˚

y˚

100˚ 65˚ O

S

R

T

Q P

ppr maths nbk

92

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 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 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

40˚ x˚ Q

A 76˚ B 52˚ C 104˚ D 90˚

xo

A 42˚ B 132˚ C 138˚ D 48˚

42˚

ppr maths nbk

93

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 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 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 65˚ B 15˚ C 50˚ D 40˚

55o

45o

y o

42o

A 100˚ B 80˚ C 115˚ D 65˚

A 84 o B 48 o C 96 o D 42 o

25

ppr maths nbk

86

5 In the diagram ABC is a tangent to the circle with centre O Find the value of a) p O b) q C B A Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip 6 In the diagram FGH is a tangent to the circle centre O at point G Find the value of y D F G H Answer helliphelliphelliphelliphelliphelliphellip 7 In the diagram PQR is a tangent to the circle centre O at point Q Find the value of

y P Q R Answer helliphelliphelliphelliphelliphelliphellip 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 S P Q R Answer helliphelliphelliphelliphelliphelliphellip

80˚

34˚ bull

p˚

q˚

100˚

40˚ y˚

E

O

y˚ O 35˚

42˚

y˚ 42˚ O

ppr maths nbk

87

9 In the diagram below PQR is a tangent to the circle centre O at point Q Find the

value of y P S Q R Answer a)helliphelliphelliphelliphelliphelliphellip 10 In the diagram EFG is a tangent to the circle FLMN Find the value of y M L G F E Answer a)helliphelliphelliphelliphelliphelliphellip

26˚ y˚

T

y˚

105˚ 35˚

ppr maths nbk

88

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 O b) q K D E F G c) r Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip c)helliphelliphelliphelliphelliphellip 2 In the diagram ABC is a tangent to the circle with centre O EODC is a straight line F Find the value of a) p E b) q D C c) r A B Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip c)helliphelliphelliphelliphelliphellip 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 b) y c) z

Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip c)helliphelliphelliphelliphelliphellip

30˚ p˚

q˚ r˚

Op˚

q˚

r˚ 48˚

bull

bull

Q P

bullx˚

y˚

z˚ 24˚

ppr maths nbk

89

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 O b) y A c) z Q T P Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip c)helliphelliphelliphelliphelliphellip 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 b) y R T S V Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip 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 Answer helliphelliphelliphelliphelliphelliphellip

x˚

y˚

z˚ 80˚

30˚

bull

O bull

x˚ y˚

34˚

75

Xo

ppr maths nbk

90

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 Answer helliphelliphelliphelliphelliphelliphellip 8 In the diagram below EFG is a tangent to the circle centre O at point F Find the value of x Answerhelliphelliphelliphelliphelliphelliphelliphellip 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 Answerhelliphelliphelliphelliphelliphelliphelliphelliphellip 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 Answer helliphelliphelliphelliphelliphelliphellip

34

xo

25 o

62 o

xo150o

25˚

ppr maths nbk

91

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 S D 100 o Q R 2 In the diagram PQ is a tangent to the circle with centre O at P Find the value of y A 40 o B 50 o C 60 o D 70 o 3 In the diagram PQ is a tangent to the circle at Q Find the value of x A 30 o B 40 o C 50 o D 80 o 4 In the diagram PQR is a tangent to the circle with centre O at Q Find the value of y A 40 o B 50 o C 65 o D 115 o

x˚ 100˚ 30˚

O bull

y˚

120˚

40˚ P

Q

S

R

PQ

R

S

T 80˚

x˚ 50˚

y˚

100˚ 65˚ O

S

R

T

Q P

ppr maths nbk

92

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 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 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

40˚ x˚ Q

A 76˚ B 52˚ C 104˚ D 90˚

xo

A 42˚ B 132˚ C 138˚ D 48˚

42˚

ppr maths nbk

93

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 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 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 65˚ B 15˚ C 50˚ D 40˚

55o

45o

y o

42o

A 100˚ B 80˚ C 115˚ D 65˚

A 84 o B 48 o C 96 o D 42 o

25

ppr maths nbk

87

9 In the diagram below PQR is a tangent to the circle centre O at point Q Find the

value of y P S Q R Answer a)helliphelliphelliphelliphelliphelliphellip 10 In the diagram EFG is a tangent to the circle FLMN Find the value of y M L G F E Answer a)helliphelliphelliphelliphelliphelliphellip

26˚ y˚

T

y˚

105˚ 35˚

ppr maths nbk

88

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 O b) q K D E F G c) r Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip c)helliphelliphelliphelliphelliphellip 2 In the diagram ABC is a tangent to the circle with centre O EODC is a straight line F Find the value of a) p E b) q D C c) r A B Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip c)helliphelliphelliphelliphelliphellip 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 b) y c) z

Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip c)helliphelliphelliphelliphelliphellip

30˚ p˚

q˚ r˚

Op˚

q˚

r˚ 48˚

bull

bull

Q P

bullx˚

y˚

z˚ 24˚

ppr maths nbk

89

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 O b) y A c) z Q T P Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip c)helliphelliphelliphelliphelliphellip 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 b) y R T S V Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip 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 Answer helliphelliphelliphelliphelliphelliphellip

x˚

y˚

z˚ 80˚

30˚

bull

O bull

x˚ y˚

34˚

75

Xo

ppr maths nbk

90

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 Answer helliphelliphelliphelliphelliphelliphellip 8 In the diagram below EFG is a tangent to the circle centre O at point F Find the value of x Answerhelliphelliphelliphelliphelliphelliphelliphellip 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 Answerhelliphelliphelliphelliphelliphelliphelliphelliphellip 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 Answer helliphelliphelliphelliphelliphelliphellip

34

xo

25 o

62 o

xo150o

25˚

ppr maths nbk

91

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 S D 100 o Q R 2 In the diagram PQ is a tangent to the circle with centre O at P Find the value of y A 40 o B 50 o C 60 o D 70 o 3 In the diagram PQ is a tangent to the circle at Q Find the value of x A 30 o B 40 o C 50 o D 80 o 4 In the diagram PQR is a tangent to the circle with centre O at Q Find the value of y A 40 o B 50 o C 65 o D 115 o

x˚ 100˚ 30˚

O bull

y˚

120˚

40˚ P

Q

S

R

PQ

R

S

T 80˚

x˚ 50˚

y˚

100˚ 65˚ O

S

R

T

Q P

ppr maths nbk

92

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 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 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

40˚ x˚ Q

A 76˚ B 52˚ C 104˚ D 90˚

xo

A 42˚ B 132˚ C 138˚ D 48˚

42˚

ppr maths nbk

93

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 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 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 65˚ B 15˚ C 50˚ D 40˚

55o

45o

y o

42o

A 100˚ B 80˚ C 115˚ D 65˚

A 84 o B 48 o C 96 o D 42 o

25

ppr maths nbk

88

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 O b) q K D E F G c) r Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip c)helliphelliphelliphelliphelliphellip 2 In the diagram ABC is a tangent to the circle with centre O EODC is a straight line F Find the value of a) p E b) q D C c) r A B Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip c)helliphelliphelliphelliphelliphellip 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 b) y c) z

Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip c)helliphelliphelliphelliphelliphellip

30˚ p˚

q˚ r˚

Op˚

q˚

r˚ 48˚

bull

bull

Q P

bullx˚

y˚

z˚ 24˚

ppr maths nbk

89

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 O b) y A c) z Q T P Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip c)helliphelliphelliphelliphelliphellip 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 b) y R T S V Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip 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 Answer helliphelliphelliphelliphelliphelliphellip

x˚

y˚

z˚ 80˚

30˚

bull

O bull

x˚ y˚

34˚

75

Xo

ppr maths nbk

90

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 Answer helliphelliphelliphelliphelliphelliphellip 8 In the diagram below EFG is a tangent to the circle centre O at point F Find the value of x Answerhelliphelliphelliphelliphelliphelliphelliphellip 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 Answerhelliphelliphelliphelliphelliphelliphelliphelliphellip 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 Answer helliphelliphelliphelliphelliphelliphellip

34

xo

25 o

62 o

xo150o

25˚

ppr maths nbk

91

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 S D 100 o Q R 2 In the diagram PQ is a tangent to the circle with centre O at P Find the value of y A 40 o B 50 o C 60 o D 70 o 3 In the diagram PQ is a tangent to the circle at Q Find the value of x A 30 o B 40 o C 50 o D 80 o 4 In the diagram PQR is a tangent to the circle with centre O at Q Find the value of y A 40 o B 50 o C 65 o D 115 o

x˚ 100˚ 30˚

O bull

y˚

120˚

40˚ P

Q

S

R

PQ

R

S

T 80˚

x˚ 50˚

y˚

100˚ 65˚ O

S

R

T

Q P

ppr maths nbk

92

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 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 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

40˚ x˚ Q

A 76˚ B 52˚ C 104˚ D 90˚

xo

A 42˚ B 132˚ C 138˚ D 48˚

42˚

ppr maths nbk

93

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 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 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 65˚ B 15˚ C 50˚ D 40˚

55o

45o

y o

42o

A 100˚ B 80˚ C 115˚ D 65˚

A 84 o B 48 o C 96 o D 42 o

25

ppr maths nbk

89

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 O b) y A c) z Q T P Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip c)helliphelliphelliphelliphelliphellip 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 b) y R T S V Answer a)helliphelliphelliphelliphelliphellip b)helliphelliphelliphelliphelliphellip 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 Answer helliphelliphelliphelliphelliphelliphellip

x˚

y˚

z˚ 80˚

30˚

bull

O bull

x˚ y˚

34˚

75

Xo

ppr maths nbk

90

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 Answer helliphelliphelliphelliphelliphelliphellip 8 In the diagram below EFG is a tangent to the circle centre O at point F Find the value of x Answerhelliphelliphelliphelliphelliphelliphelliphellip 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 Answerhelliphelliphelliphelliphelliphelliphelliphelliphellip 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 Answer helliphelliphelliphelliphelliphelliphellip

34

xo

25 o

62 o

xo150o

25˚

ppr maths nbk

91

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 S D 100 o Q R 2 In the diagram PQ is a tangent to the circle with centre O at P Find the value of y A 40 o B 50 o C 60 o D 70 o 3 In the diagram PQ is a tangent to the circle at Q Find the value of x A 30 o B 40 o C 50 o D 80 o 4 In the diagram PQR is a tangent to the circle with centre O at Q Find the value of y A 40 o B 50 o C 65 o D 115 o

x˚ 100˚ 30˚

O bull

y˚

120˚

40˚ P

Q

S

R

PQ

R

S

T 80˚

x˚ 50˚

y˚

100˚ 65˚ O

S

R

T

Q P

ppr maths nbk

92

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 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 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

40˚ x˚ Q

A 76˚ B 52˚ C 104˚ D 90˚

xo

A 42˚ B 132˚ C 138˚ D 48˚

42˚

ppr maths nbk

93

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 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 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 65˚ B 15˚ C 50˚ D 40˚

55o

45o

y o

42o

A 100˚ B 80˚ C 115˚ D 65˚

A 84 o B 48 o C 96 o D 42 o

25

ppr maths nbk

90

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 Answer helliphelliphelliphelliphelliphelliphellip 8 In the diagram below EFG is a tangent to the circle centre O at point F Find the value of x Answerhelliphelliphelliphelliphelliphelliphelliphellip 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 Answerhelliphelliphelliphelliphelliphelliphelliphelliphellip 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 Answer helliphelliphelliphelliphelliphelliphellip

34

xo

25 o

62 o

xo150o

25˚

ppr maths nbk

91

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 S D 100 o Q R 2 In the diagram PQ is a tangent to the circle with centre O at P Find the value of y A 40 o B 50 o C 60 o D 70 o 3 In the diagram PQ is a tangent to the circle at Q Find the value of x A 30 o B 40 o C 50 o D 80 o 4 In the diagram PQR is a tangent to the circle with centre O at Q Find the value of y A 40 o B 50 o C 65 o D 115 o

x˚ 100˚ 30˚

O bull

y˚

120˚

40˚ P

Q

S

R

PQ

R

S

T 80˚

x˚ 50˚

y˚

100˚ 65˚ O

S

R

T

Q P

ppr maths nbk

92

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 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 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

40˚ x˚ Q

A 76˚ B 52˚ C 104˚ D 90˚

xo

A 42˚ B 132˚ C 138˚ D 48˚

42˚

ppr maths nbk

93

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 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 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 65˚ B 15˚ C 50˚ D 40˚

55o

45o

y o

42o

A 100˚ B 80˚ C 115˚ D 65˚

A 84 o B 48 o C 96 o D 42 o

25

ppr maths nbk

91

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 S D 100 o Q R 2 In the diagram PQ is a tangent to the circle with centre O at P Find the value of y A 40 o B 50 o C 60 o D 70 o 3 In the diagram PQ is a tangent to the circle at Q Find the value of x A 30 o B 40 o C 50 o D 80 o 4 In the diagram PQR is a tangent to the circle with centre O at Q Find the value of y A 40 o B 50 o C 65 o D 115 o

x˚ 100˚ 30˚

O bull

y˚

120˚

40˚ P

Q

S

R

PQ

R

S

T 80˚

x˚ 50˚

y˚

100˚ 65˚ O

S

R

T

Q P

ppr maths nbk

92

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 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 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

40˚ x˚ Q

A 76˚ B 52˚ C 104˚ D 90˚

xo

A 42˚ B 132˚ C 138˚ D 48˚

42˚

ppr maths nbk

93

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 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 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 65˚ B 15˚ C 50˚ D 40˚

55o

45o

y o

42o

A 100˚ B 80˚ C 115˚ D 65˚

A 84 o B 48 o C 96 o D 42 o

25

ppr maths nbk

92

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 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 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

40˚ x˚ Q

A 76˚ B 52˚ C 104˚ D 90˚

xo

A 42˚ B 132˚ C 138˚ D 48˚

42˚

ppr maths nbk

93

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 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 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 65˚ B 15˚ C 50˚ D 40˚

55o

45o

y o

42o

A 100˚ B 80˚ C 115˚ D 65˚

A 84 o B 48 o C 96 o D 42 o

25

ppr maths nbk

93

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 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 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 65˚ B 15˚ C 50˚ D 40˚

55o

45o

y o

42o

A 100˚ B 80˚ C 115˚ D 65˚

A 84 o B 48 o C 96 o D 42 o

25