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)

d

=

√

(

l

2

+

r

2

)
(iii)

d

=

√

(

l

2

−

r

2

)
(iv)

l

=

√

(

d

2

+

r

2

)
(v)

r

=

√

(

l

2

+

d

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)

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 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)

√

d

2

−

(

r

1

+

r

2

)

2
(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)

None of these

Question 5

5.

Two circles with equal radii are

(i)

only similar but not congruent
(ii)

congruent
(iii)

concentric
(iv)

not similar

Question 6

6.

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

(i)

95°
(ii)

120°
(iii)

100°
(iv)

90°
(v)

105°

Question 7

7.

If two circles of radii 15 cm and 4 cm touch internally, the distance between their centres is

(i)

10 cm
(ii)

9 cm
(iii)

11 cm
(iv)

12 cm
(v)

13 cm

Question 8

8.

If two circles of radii 12 cm and 6 cm touch externally, the distance between their centres is

(i)

20 cm
(ii)

16 cm
(iii)

19 cm
(iv)

18 cm
(v)

17 cm

Question 9

9.

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

(i)

2
(ii)

0
(iii)

(-2)
(iv)

1
(v)

4

Question 10

10.

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

(i)

1
(ii)

2
(iii)

3
(iv)

4
(v)

0

Question 11

11.

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

(i)

4
(ii)

6
(iii)

0
(iv)

3
(v)

2

Question 12

12.

In the given figure, O is the centre of the circle and LM is the tangent at I. If ∠JIK = 47° and ∠LIJ = 94°, find ∠IKJ

(i)

52°
(ii)

62°
(iii)

57°
(iv)

47°
(v)

77°

Question 13

13.

In the given figure, O is the centre of the circle and FG is the tangent at C. If ∠DCE = 45° and ∠FCD = 40°, find ∠ECG

(i)

105°
(ii)

95°
(iii)

110°
(iv)

125°
(v)

100°

Question 14

14.

In the given figure, O is the centre of the circle and GI is the tangent at H . If ∠FEH = 26°, find ∠FGH

(i)

38°
(ii)

68°
(iii)

53°
(iv)

43°
(v)

48°

Question 15

15.

In the given figure, O is the centre of the circle and IK is the tangent at J. If ∠HGJ = 26°, find ∠HIJ + ∠HJI

(i)

94°
(ii)

79°
(iii)

74°
(iv)

64°
(v)

69°

Question 16

16.

In the given figure, O is the centre of the circle and KL is the tangent at G. If ∠GJI = 53°, find ∠GHI

(i)

137°
(ii)

142°
(iii)

127°
(iv)

132°
(v)

157°

Question 17

17.

In the given figure, O is the centre of the circle and HI is the tangent at D. If ∠DGF = 51°, find ∠IDF

(i)

61°
(ii)

81°
(iii)

51°
(iv)

66°
(v)

56°

Question 18

18.

In the given figure, O is the centre of the circle and HI is the tangent at E. If ∠GEF = 52° and ∠FEI = 44°, find ∠GFE

(i)

89°
(ii)

114°
(iii)

84°
(iv)

94°
(v)

99°

Question 19

19.

In the given figure, O is the centre of the circle and EF is the tangent at D. If ∠DCB = 32°, find ∠FDB

(i)

42°
(ii)

47°
(iii)

62°
(iv)

37°
(v)

32°

Question 20

20.

In the given figure, O is the centre of the circle and JK is the tangent at I. If ∠IGH = 55°, find ∠JIH

(i)

65°
(ii)

55°
(iii)

60°
(iv)

70°
(v)

85°

Question 21

21.

In the given figure, O is the centre of the circle and EF is the tangent at D. If ∠CAD = 30° and ∠ACB = 46°, find ∠FDA

(i)

60°
(ii)

70°
(iii)

65°
(iv)

90°
(v)

75°

Question 22

22.

In the given figure, O is the centre of the circle and KL is the tangent at J. If ∠IGJ = 56° and ∠GIH = 49°, find ∠IGH

(i)

56°
(ii)

51°
(iii)

41°
(iv)

46°
(v)

71°

Question 23

23.

In the given figure, O is the centre of the circle and KL is the tangent at J. If ∠IGJ = 35° and ∠GIH = 57°, find ∠KJI

(i)

40°
(ii)

65°
(iii)

45°
(iv)

50°
(v)

35°

Question 24

24.

In the given figure, O is the centre of the circle and JK is the tangent at G. If ∠OHG = 40°, find ∠KGH

(i)

55°
(ii)

65°
(iii)

60°
(iv)

50°
(v)

80°

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 = 56°, find ∠GOI

(i)

122°
(ii)

112°
(iii)

117°
(iv)

142°
(v)

127°

Question 26

26.

In the given figure, O is the centre of the circle and the tangents IL and KL meet at point L. If ∠JKI = 48°, find ∠KLI

(i)

114°
(ii)

84°
(iii)

94°
(iv)

99°
(v)

89°

Question 27

27.

In the given figure, O is the centre of the circle and CE is the tangent at D. If ∠DEF = 51°,∠EDF = 33°, find ∠HDC

(i)

94°
(ii)

114°
(iii)

84°
(iv)

99°
(v)

89°

Question 28

28.

Which of the following statements are true?

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

(i)

{e,b}
(ii)

{a,b,d}
(iii)

{c,e,d}
(iv)

{c,a}
(v)

{c,a,b}

Question 29

29.

Which of the following statements are true?

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

(i)

{b,a}
(ii)

{c,d,a}
(iii)

{e,b,a}
(iv)

{a,d}
(v)

{c,d}

Question 30

30.

O is the centre of the circumcircle of △HIJ. Tangents at H and I intersect at K. If ∠HKI = 64.62° and ∠HOJ = 130°, find ∠JHI

(i)

72.31°
(ii)

87.31°
(iii)

67.31°
(iv)

62.31°
(v)

57.31°

Question 31

31.

O is the centre of the circumcircle of △DEF. Tangents at D and F intersect at G. If ∠DGF = 69.7°, find ∠FED

(i)

65.15°
(ii)

70.15°
(iii)

55.15°
(iv)

60.15°
(v)

85.15°

Question 32

32.

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

(i)

quadrant
(ii)

semi-circle
(iii)

radius
(iv)

segment
(v)

secant

Question 33

33.

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

(i)

quadrant
(ii)

segment
(iii)

major segment
(iv)

radius
(v)

tangent

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)

centre
(ii)

secant
(iii)

quadrant
(iv)

segment
(v)

tangent

Question 35

35.

Which of the following statements are true?

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

(i)

{b,a}
(ii)

{a,c}
(iii)

{b,d,a}
(iv)

{d,c}
(v)

{b,c,a}

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 diameter is a limiting case of a chord.
d)	A tangent is the limiting case of a secant.
e)	A secant and a chord are same.

(i)

{e,a,c}
(ii)

{b,d}
(iii)

{c,d}
(iv)

{a,c}
(v)

{b,d,c}

Question 37

37.

Which of the following statements are true?

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

(i)

{c,d}
(ii)

{a,b}
(iii)

{b,d,e}
(iv)

{a,b,d}
(v)

{a,c,e}

Question 38

38.

Which of the following statements are true?

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

(i)

{b,d,e}
(ii)

{a,b}
(iii)

{a,c,e}
(iv)

{a,b,d}
(v)

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

(i)

{a,b,c}
(ii)

{a,c}
(iii)

{a,b}
(iv)

{b,c,d}
(v)

{a,d}

Question 40

40.

Which of the following statements are true?

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

(i)

{a,e}
(ii)

{c,d,e}
(iii)

{b,f}
(iv)

{e,f}
(v)

{a,f,e}

Question 41

41.

Two circles are of radii 3 cm and 6 cm. If the distance between their centres is 10 cm, what is the length of their direct common tangent?

(i)

7.54 cm
(ii)

9.54 cm
(iii)

8.54 cm
(iv)

11.54 cm
(v)

10.54 cm

Question 42

42.

Two circles are of radii 5 cm and 5 cm. If the distance between their centres is 16 cm, what is the length of their transverse common tangent?

(i)

12.49 cm
(ii)

10.49 cm
(iii)

14.49 cm
(iv)

13.49 cm
(v)

11.49 cm

Question 43

43.

In the given figure, ABCD is a cyclic quadrilateral such that CA bisects ∠DAB and EF is the tangent at C. If ∠CAB = 53°, find ∠ECB

(i)

63°
(ii)

53°
(iii)

68°
(iv)

83°
(v)

58°

Question 44

44.

In the given figure, O is the centre of the circle and CE is the tangent at D. If ∠DEF = 32°,∠EDF = 40°, find ∠GDF

(i)

73°
(ii)

98°
(iii)

83°
(iv)

68°
(v)

78°

Question 45

45.

In the given figure, JH and JI are tangent segments to the circle with centre O. Given ∠IJK = 21°, find ∠HIO

(i)

36°
(ii)

51°
(iii)

21°
(iv)

31°
(v)

26°

Question 46

46.

In the given figure, EC and ED are tangent segments to the circle with centre O. Given ∠DEF = 34°, find ∠CDF

(i)

38°
(ii)

43°
(iii)

58°
(iv)

33°
(v)

28°

Question 47

47.

With the vertices of a triangle △FGH as centres, three circles are drawn touching each other externally. If the sides of the triangle are 10 cm , 13 cm and 13 cm , find the radii of the circles

(i)

10 cm , 5 cm & 8 cm respectively
(ii)

5 cm , 10 cm & 8 cm respectively
(iii)

5 cm , 5 cm & 13 cm respectively
(iv)

5 cm , 5 cm & 8 cm respectively
(v)

10 cm , 10 cm & 13 cm respectively

Question 48

48.

O is the centre of the circle. BC and DC are tangents to the circle. If ∠DEB = 33.5°, find ∠BCD

(i)

113°
(ii)

143°
(iii)

118°
(iv)

128°
(v)

123°

Question 49

49.

In the given figure, DE and FG are parallel tangents to the circle with centre O. DG is another tangent meeting DE and FG at D and G. Find ∠DOG

(i)

100°
(ii)

90°
(iii)

105°
(iv)

120°
(v)

95°

Question 50

50.

In the given figure, FI is the common tangent to the two circles. FG & FH are also tangents. Given FG = 9 cm, find FH

(i)

9 cm
(ii)

11 cm
(iii)

10 cm
(iv)

7 cm
(v)

8 cm

Question 51

51.

EF is a line segment and H is its mid-point. Three semi-circles are drawn with EH , HF and EF as diameters. G , I and H respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given EG = 7 cm

(i)

6.67 cm
(ii)

5.67 cm
(iii)

2.67 cm
(iv)

3.67 cm
(v)

4.67 cm

Question 52

52.

In the given figure, two circles intersect at points I & J. A tangent is drawn at point K. From the same point, two lines are drawn passing through points I & J. They meet the other end of the second circle at H & G. Given ∠K = 60°, find ∠GHI

(i)

75°
(ii)

65°
(iii)

90°
(iv)

70°
(v)

60°

Question 53

53.

In the given figure, two circles intersect at points G & H. A tangent is drawn at point I. From the same point, two lines are drawn passing through points G & H. They meet the other end of the second circle at F & E. Given ∠I = 91°, find ∠FEH

(i)

121°
(ii)

96°
(iii)

101°
(iv)

91°
(v)

106°

Question 54

54.

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

(i)

149°
(ii)

119°
(iii)

124°
(iv)

134°
(v)

129°

Question 55

55.

In the given figure, two circles intersect at points K & L. A tangent is drawn at point M. From the same point, two lines are drawn passing through points K & L. They meet the other end of the second circle at J & I. Given ∠M = 84°, find ∠JKL

(i)

106°
(ii)

96°
(iii)

111°
(iv)

126°
(v)

101°

Question 56

56.

In the given figure, FS & GS are tangents to the circle with centre O. Given ∠F = 24°, find ∠S

(i)

58°
(ii)

48°
(iii)

63°
(iv)

78°
(v)

53°

Question 57

57.

In the given figure, EQ & FQ are tangents to the circle with centre O. Given OE = 15 cm and EF = 28 cm, find EQ

(i)

37.00 cm
(ii)

40.00 cm
(iii)

39.00 cm
(iv)

41.00 cm
(v)

38.00 cm

Question 58

58.

In the given figure, GR & HR are tangents to the circle with centre O. Given ∠GOH = 119°, find ∠GRH

(i)

91°
(ii)

76°
(iii)

71°
(iv)

66°
(v)

61°

Assignment Key