EduSahara™ Worksheet

Question 1

1.

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 2

2.

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

(i)

105°
(ii)

100°
(iii)

90°
(iv)

120°
(v)

95°

Question 3

3.

If two circles of radii 10 cm and 5 cm touch externally, the distance between their centres is

(i)

14 cm
(ii)

15 cm
(iii)

13 cm
(iv)

17 cm
(v)

16 cm

Question 4

4.

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

(i)

1
(ii)

4
(iii)

0
(iv)

(-1)
(v)

2

Question 5

5.

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

(i)

2
(ii)

0
(iii)

1
(iv)

3
(v)

4

Question 6

6.

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

(i)

2
(ii)

3
(iii)

4
(iv)

5
(v)

1

Question 7

7.

In the given figure, O is the centre of the circle and JK is the tangent at I. If ∠HFI = 51° and ∠FHG = 56°, find ∠HFG

(i)

39°
(ii)

44°
(iii)

34°
(iv)

49°
(v)

64°

Question 8

8.

In the given figure, O is the centre of the circle and GH is the tangent at D. If ∠OED = 33°, find ∠HDE

(i)

87°
(ii)

72°
(iii)

67°
(iv)

62°
(v)

57°

Question 9

9.

In the given figure, O is the centre of the circle and the tangents AD and CD meet at point D. If ∠BCA = 59°, find ∠AOC

(i)

118°
(ii)

123°
(iii)

148°
(iv)

133°
(v)

128°

Question 10

10.

In the given figure, O is the centre of the circle and the tangents IL and KL meet at point L. If ∠JKI = 50°, find ∠KLI

(i)

90°
(ii)

85°
(iii)

110°
(iv)

95°
(v)

80°

Question 11

11.

In the given figure, O is the centre of the circle and FH is the tangent at G. If ∠GHI = 45°,∠HGI = 34°, find ∠KGF

(i)

109°
(ii)

89°
(iii)

84°
(iv)

79°
(v)

94°

Question 12

12.

In the given figure, HIJK is a cyclic quadrilateral such that JH bisects ∠KHI and LM is the tangent at J. If ∠JHI = 59°, find ∠LJI

(i)

59°
(ii)

69°
(iii)

74°
(iv)

64°
(v)

89°

Question 13

13.

In the given figure, O is the centre of the circle and FH is the tangent at G. If ∠GHI = 37°,∠HGI = 35°, find ∠JGI

(i)

103°
(ii)

78°
(iii)

73°
(iv)

83°
(v)

88°

Question 14

14.

In the given figure, KI and KJ are tangent segments to the circle with centre O. Given ∠JKL = 22°, find ∠IJO

(i)

27°
(ii)

32°
(iii)

52°
(iv)

37°
(v)

22°

Question 15

15.

In the given figure, HF and HG are tangent segments to the circle with centre O. Given ∠GHI = 37°, find ∠FGI

(i)

26.5°
(ii)

31.5°
(iii)

41.5°
(iv)

56.5°
(v)

36.5°

Question 16

16.

O is the centre of the circle. JK and LK are tangents to the circle. If ∠LMJ = 40°, find ∠JKL

(i)

100°
(ii)

105°
(iii)

130°
(iv)

110°
(v)

115°

Question 17

17.

In the given figure, BC and DE are parallel tangents to the circle with centre O. BE is another tangent meeting BC and DE at B and E. Find ∠BOE

(i)

95°
(ii)

100°
(iii)

105°
(iv)

90°
(v)

120°

Question 18

18.

In the given figure, DG is the common tangent to the two circles. DE & DF are also tangents. Given DE = 13 cm, find DF

(i)

13 cm
(ii)

12 cm
(iii)

15 cm
(iv)

14 cm
(v)

11 cm

Question 19

19.

AB is a line segment and D is its mid-point. Three semi-circles are drawn with AD , DB and AB as diameters. C , E and D respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given AC = 5 cm

(i)

3.33 cm
(ii)

2.33 cm
(iii)

4.33 cm
(iv)

5.33 cm
(v)

1.33 cm

Question 20

20.

In the given figure, CS & DS are tangents to the circle with centre O. Given ∠C = 30°, find ∠S

(i)

65°
(ii)

75°
(iii)

70°
(iv)

90°
(v)

60°

Question 21

21.

In the given figure, DS & ES are tangents to the circle with centre O. Given OD = 15 cm and DE = 28 cm, find DS

(i)

41.00 cm
(ii)

37.00 cm
(iii)

38.00 cm
(iv)

40.00 cm
(v)

39.00 cm

Question 22

22.

In the given figure, FT & GT are tangents to the circle with centre O. Given ∠FTG = 54°, find ∠FOG

(i)

156°
(ii)

141°
(iii)

131°
(iv)

136°
(v)

126°

Assignment Key