EduSahara™ Worksheet

Question 1

1.

If 'l' is the length of the tangent drawn to a circle with radius 'r' from point 'P' which is 'd' cm away from the centre, then

(i)

l

=

√

(

d

2

+

r

2

)
(ii)

l

=

√

(

d

2

−

r

2

)
(iii)

r

=

√

(

l

2

+

d

2

)
(iv)

d

=

√

(

l

2

+

r

2

)
(v)

d

=

√

(

l

2

−

r

2

)

Question 2

2.

Two circles with radii R and r touch internally. If the distance between their centres is d, then

(i)

d < R + r
(ii)

d = R - r
(iii)

d = R + r
(iv)

d > R - r
(v)

d < R - r

Question 3

3.

The distance between the centres of two circles is
d
.

If the radii are
r

1
and
r

2
,
the length of their transverse common tangent is

(i)

√

d

2

+

(

r

1

+

r

2

)

2
(ii)

None of these
(iii)

√

d

2

+

(

r

1

−

r

2

)

2
(iv)

√

d

2

−

(

r

1

−

r

2

)

2
(v)

√

d

2

−

(

r

1

+

r

2

)

2

Question 4

4.

The distance between the centres of two circles is
d
.

If the radii are
r

1
and
r

2
,
the length of their direct common tangent is

(i)

None of these
(ii)

√

d

2

+

(

r

1

+

r

2

)

2
(iii)

√

d

2

+

(

r

1

−

r

2

)

2
(iv)

√

d

2

−

(

r

1

−

r

2

)

2
(v)

√

d

2

−

(

r

1

+

r

2

)

2

Question 5

5.

Two circles with equal radii are

(i)

concentric
(ii)

only similar but not congruent
(iii)

not similar
(iv)

congruent

Question 6

6.

The angle between a tangent to a circle and the radius drawn at the point of contact is

(i)

120°
(ii)

100°
(iii)

95°
(iv)

90°
(v)

105°

Question 7

7.

If two circles of radii 8 cm and 7 cm touch internally, the distance between their centres is

(i)

2 cm
(ii)

1 cm
(iii)

3 cm
(iv)

9 cm
(v)

0 cm

Question 8

8.

If two circles of radii 13 cm and 7 cm touch externally, the distance between their centres is

(i)

20 cm
(ii)

18 cm
(iii)

21 cm
(iv)

22 cm
(v)

19 cm

Question 9

9.

If two circles
touch internally
,
the number of their common tangents is

(i)

(-2)
(ii)

2
(iii)

4
(iv)

0
(v)

1

Question 10

10.

If two circles
intersect
,
the number of their common tangents is

(i)

3
(ii)

(-1)
(iii)

2
(iv)

1
(v)

4

Question 11

11.

If two circles
touch externally
,
the number of their common tangents is

(i)

4
(ii)

3
(iii)

0
(iv)

2
(v)

5

Question 12

12.

In the given figure, O is the centre of the circle and KL is the tangent at H. If ∠IHJ = 57° and ∠KHI = 102°, find ∠HJI

(i)

50°
(ii)

55°
(iii)

60°
(iv)

45°
(v)

75°

Question 13

13.

In the given figure, O is the centre of the circle and IJ is the tangent at F. If ∠GFH = 36° and ∠IFG = 41°, find ∠HFJ

(i)

108°
(ii)

118°
(iii)

103°
(iv)

113°
(v)

133°

Question 14

14.

In the given figure, O is the centre of the circle and EG is the tangent at F . If ∠DCF = 29°, find ∠DEF

(i)

37°
(ii)

42°
(iii)

32°
(iv)

62°
(v)

47°

Question 15

15.

In the given figure, O is the centre of the circle and JL is the tangent at K. If ∠IHK = 29°, find ∠IJK + ∠IKJ

(i)

66°
(ii)

71°
(iii)

61°
(iv)

91°
(v)

76°

Question 16

16.

In the given figure, O is the centre of the circle and EF is the tangent at A. If ∠ADC = 41°, find ∠ABC

(i)

154°
(ii)

139°
(iii)

169°
(iv)

144°
(v)

149°

Question 17

17.

In the given figure, O is the centre of the circle and FG is the tangent at B. If ∠BED = 54°, find ∠GBD

(i)

54°
(ii)

84°
(iii)

69°
(iv)

59°
(v)

64°

Question 18

18.

In the given figure, O is the centre of the circle and HI is the tangent at E. If ∠GEF = 40° and ∠FEI = 33°, find ∠GFE

(i)

122°
(ii)

107°
(iii)

117°
(iv)

137°
(v)

112°

Question 19

19.

In the given figure, O is the centre of the circle and DE is the tangent at C. If ∠CBA = 38°, find ∠ECA

(i)

43°
(ii)

68°
(iii)

48°
(iv)

38°
(v)

53°

Question 20

20.

In the given figure, O is the centre of the circle and JK is the tangent at I. If ∠IGH = 43°, find ∠JIH

(i)

53°
(ii)

73°
(iii)

48°
(iv)

43°
(v)

58°

Question 21

21.

In the given figure, O is the centre of the circle and LM is the tangent at K. If ∠JHK = 41° and ∠HJI = 51°, find ∠MKH

(i)

64°
(ii)

79°
(iii)

59°
(iv)

54°
(v)

49°

Question 22

22.

In the given figure, O is the centre of the circle and JK is the tangent at I. If ∠HFI = 43° and ∠FHG = 50°, find ∠HFG

(i)

55°
(ii)

40°
(iii)

45°
(iv)

70°
(v)

50°

Question 23

23.

In the given figure, O is the centre of the circle and KL is the tangent at J. If ∠IGJ = 42° and ∠GIH = 42°, find ∠KJI

(i)

42°
(ii)

57°
(iii)

47°
(iv)

72°
(v)

52°

Question 24

24.

In the given figure, O is the centre of the circle and EF is the tangent at B. If ∠OCB = 33.5°, find ∠FBC

(i)

56.5°
(ii)

61.5°
(iii)

66.5°
(iv)

71.5°
(v)

86.5°

Question 25

25.

In the given figure, O is the centre of the circle and the tangents GJ and IJ meet at point J. If ∠HIG = 54°, find ∠GOI

(i)

118°
(ii)

113°
(iii)

108°
(iv)

138°
(v)

123°

Question 26

26.

In the given figure, O is the centre of the circle and the tangents BE and DE meet at point E. If ∠CDB = 54°, find ∠DEB

(i)

87°
(ii)

77°
(iii)

102°
(iv)

82°
(v)

72°

Question 27

27.

In the given figure, O is the centre of the circle and IK is the tangent at J. If ∠JKL = 51°,∠KJL = 31°, find ∠NJI

(i)

82°
(ii)

112°
(iii)

92°
(iv)

87°
(v)

97°

Question 28

28.

Which of the following statements are true?

a)	One and only one tangent can be drawn to a circle from a point outside it.
b)	An infinite number of diameters may be drawn for a circle.
c)	Two semi-circles of a circle together make the whole circle.
d)	Every circle has a unique diameter.
e)	An infinite number of chords may be drawn for a circle.

(i)

{a,b}
(ii)

{d,c}
(iii)

{a,b,c}
(iv)

{a,d,e}
(v)

{b,c,e}

Question 29

29.

Which of the following statements are true?

a)	Every circle has a unique diameter.
b)	One and only one tangent can be drawn to pass through a point on a circle.
c)	Diameter of a circle is a part of the semi-circle of the circle.
d)	One and only one tangent can be drawn to a circle from a point outside it.
e)	A secant of a circle is a segment having its end points on the circle.

(i)

{d,c,b}
(ii)

{e,a,b}
(iii)

{b,c}
(iv)

{a,b}
(v)

{d,c}

Question 30

30.

O is the centre of the circumcircle of △EFG. Tangents at E and F intersect at H. If ∠EHF = 54.57° and ∠EOG = 110°, find ∠GEF

(i)

92.28°
(ii)

67.28°
(iii)

77.28°
(iv)

62.28°
(v)

72.28°

Question 31

31.

O is the centre of the circumcircle of △IJK. Tangents at I and K intersect at L. If ∠ILK = 50.34°, find ∠KJI

(i)

74.83°
(ii)

94.83°
(iii)

79.83°
(iv)

69.83°
(v)

64.83°

Question 32

32.

A line which intersects the circle at two distinct points is called a

(i)

circumference
(ii)

secant
(iii)

major segment
(iv)

diameter
(v)

tangent

Question 33

33.

A line which touches a circle at only one point is called a

(i)

tangent
(ii)

centre
(iii)

semi-circle
(iv)

quadrant
(v)

secant

Question 34

34.

If the two radii OP and OQ of a circle are at right angles to each other, then the sector OPQ is called a

(i)

circumference
(ii)

centre
(iii)

major segment
(iv)

quadrant
(v)

radius

Question 35

35.

Which of the following statements are true?

a)	Atmost one common tangent can be drawn for any two concentric circles.
b)	Atmost two common tangents can be drawn touching any two circles.
c)	A maximum of four common tangents can be drawn touching any two circles.
d)	Atmost three common tangents can be drawn touching two circles which touch each other.

(i)

{c,d}
(ii)

{a,b,c}
(iii)

{b,d}
(iv)

{a,d,c}
(v)

{a,c}

Question 36

36.

Which of the following statements are true?

a)	A radius is a limiting case of a diameter.
b)	A secant has two end points.
c)	A tangent is the limiting case of a secant.
d)	A diameter is a limiting case of a chord.
e)	A secant and a chord are same.

(i)

{b,d,c}
(ii)

{e,a,c}
(iii)

{b,d}
(iv)

{c,d}
(v)

{a,c}

Question 37

37.

Which of the following statements are true?

a)	Only one tangent can be drawn through a point on a circle.
b)	Atmost one tangent can be drawn through a point inside the circle.
c)	The sides of a triangle can be tangents to a circle.
d)	Two tangents to a circle always intersect.
e)	Only two tangents can be drawn from a point outside the circle.

(i)

{d,c}
(ii)

{b,a,c}
(iii)

{a,c,e}
(iv)

{b,d,e}
(v)

{b,a}

Question 38

38.

Which of the following statements are true?

a)	If two tangents are perpendicular, they form a right angled triangle with their points of contact with the circle and their point of intersection.
b)	Two different tangents can meet at a point on the circle.
c)	If two tangents to a circle intersect, their points of contact with the circle together with their point of intersection form an isosceles triangle.
d)	If two tangents are parallel, the distance between them is equal to the diameter of the circle.
e)	A line parallel to a tangent is a secant.

(i)

{e,c}
(ii)

{a,c,d}
(iii)

{b,a}
(iv)

{b,a,c}
(v)

{b,e,d}

Question 39

39.

Which of the following statements are true?

a)	If two circles touch each other externally, there is only one common tangent.
b)	If two circles intersect, then two common tangents can be drawn.
c)	If two circles touch each other internally, there is only one common tangent.
d)	There exists four common tangents for any two non-intersecting circles.

(i)

{a,c}
(ii)

{b,c,d}
(iii)

{a,b}
(iv)

{a,d}
(v)

{a,b,c}

Question 40

40.

Which of the following statements are true?

a)	If two circles touch externally, the distance between their centres is the sum of their radii.
b)	If two circles touch externally, their centres and the point of contact form an isosceles triangle.
c)	If two circles touch internally, their centres and the point of contact form a scalene triangle.
d)	If two circles touch internally, the distance between their centres is the difference of their radii.
e)	If two circles touch internally, the square of the distance between their centres is the difference of the squares of their radii.
f)	If two circles touch externally, the square of the distance between their centres is the sum of the squares of their radii.

(i)

{b,a}
(ii)

{e,f,a}
(iii)

{b,d,a}
(iv)

{c,d}
(v)

{a,d}

Question 41

41.

Two circles are of radii 5 cm and 4 cm. If the distance between their centres is 14 cm, what is the length of their direct common tangent?

(i)

15.96 cm
(ii)

12.96 cm
(iii)

11.96 cm
(iv)

14.96 cm
(v)

13.96 cm

Question 42

42.

Two circles are of radii 1 cm and 6 cm. If the distance between their centres is 9 cm, what is the length of their transverse common tangent?

(i)

5.66 cm
(ii)

3.66 cm
(iii)

4.66 cm
(iv)

7.66 cm
(v)

6.66 cm

Question 43

43.

In the given figure, JKLM is a cyclic quadrilateral such that LJ bisects ∠MJK and NO is the tangent at L. If ∠LJK = 50°, find ∠NLK

(i)

80°
(ii)

65°
(iii)

55°
(iv)

50°
(v)

60°

Question 44

44.

In the given figure, O is the centre of the circle and CE is the tangent at D. If ∠DEF = 38°,∠EDF = 34°, find ∠GDF

(i)

84°
(ii)

104°
(iii)

89°
(iv)

79°
(v)

74°

Question 45

45.

In the given figure, IG and IH are tangent segments to the circle with centre O. Given ∠HIJ = 32°, find ∠GHO

(i)

37°
(ii)

32°
(iii)

42°
(iv)

47°
(v)

62°

Question 46

46.

In the given figure, EC and ED are tangent segments to the circle with centre O. Given ∠DEF = 28°, find ∠CDF

(i)

36°
(ii)

46°
(iii)

31°
(iv)

41°
(v)

61°

Question 47

47.

With the vertices of a triangle △ABC as centres, three circles are drawn touching each other externally. If the sides of the triangle are 10 cm , 16 cm and 12 cm , find the radii of the circles

(i)

3 cm , 7 cm & 9 cm respectively
(ii)

8 cm , 7 cm & 9 cm respectively
(iii)

3 cm , 7 cm & 14 cm respectively
(iv)

8 cm , 12 cm & 14 cm respectively
(v)

3 cm , 12 cm & 9 cm respectively

Question 48

48.

O is the centre of the circle. EF and GF are tangents to the circle. If ∠GHE = 43.5°, find ∠EFG

(i)

123°
(ii)

98°
(iii)

93°
(iv)

108°
(v)

103°

Question 49

49.

In the given figure, GH and IJ are parallel tangents to the circle with centre O. GJ is another tangent meeting GH and IJ at G and J. Find ∠GOJ

(i)

105°
(ii)

90°
(iii)

95°
(iv)

120°
(v)

100°

Question 50

50.

In the given figure, CF is the common tangent to the two circles. CD & CE are also tangents. Given CD = 11 cm, find CE

(i)

12 cm
(ii)

11 cm
(iii)

13 cm
(iv)

10 cm
(v)

9 cm

Question 51

51.

JK is a line segment and M is its mid-point. Three semi-circles are drawn with JM , MK and JK as diameters. L , N and M respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given JL = 8 cm

(i)

3.33 cm
(ii)

7.33 cm
(iii)

5.33 cm
(iv)

4.33 cm
(v)

6.33 cm

Question 52

52.

In the given figure, two circles intersect at points D & E. A tangent is drawn at point F. From the same point, two lines are drawn passing through points D & E. They meet the other end of the second circle at C & B. Given ∠F = 65°, find ∠BCD

(i)

65°
(ii)

70°
(iii)

95°
(iv)

75°
(v)

80°

Question 53

53.

In the given figure, two circles intersect at points E & F. A tangent is drawn at point G. From the same point, two lines are drawn passing through points E & F. They meet the other end of the second circle at D & C. Given ∠G = 89°, find ∠DCF

(i)

89°
(ii)

99°
(iii)

104°
(iv)

94°
(v)

119°

Question 54

54.

In the given figure, two circles intersect at points D & E. A tangent is drawn at point F. From the same point, two lines are drawn passing through points D & E. They meet the other end of the second circle at C & B. Given ∠F = 61°, find ∠BED

(i)

119°
(ii)

149°
(iii)

124°
(iv)

129°
(v)

134°

Question 55

55.

In the given figure, two circles intersect at points D & E. A tangent is drawn at point F. From the same point, two lines are drawn passing through points D & E. They meet the other end of the second circle at C & B. Given ∠F = 85°, find ∠CDE

(i)

105°
(ii)

95°
(iii)

100°
(iv)

125°
(v)

110°

Question 56

56.

In the given figure, GS & HS are tangents to the circle with centre O. Given ∠G = 30°, find ∠S

(i)

90°
(ii)

75°
(iii)

65°
(iv)

70°
(v)

60°

Question 57

57.

In the given figure, GR & HR are tangents to the circle with centre O. Given OG = 11 cm and GH = 19 cm, find GR

(i)

18.84 cm
(ii)

19.84 cm
(iii)

16.84 cm
(iv)

20.84 cm
(v)

17.84 cm

Question 58

58.

In the given figure, BQ & CQ are tangents to the circle with centre O. Given ∠BOC = 118°, find ∠BQC

(i)

62°
(ii)

67°
(iii)

77°
(iv)

92°
(v)

72°

Assignment Key