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)

100°
(ii)

90°
(iii)

120°
(iv)

95°
(v)

105°

Question 3

3.

If two circles of radii 14 cm and 7 cm touch externally, the distance between their centres is

(i)

21 cm
(ii)

23 cm
(iii)

22 cm
(iv)

19 cm
(v)

20 cm

Question 4

4.

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

(i)

0
(ii)

4
(iii)

(-1)
(iv)

1
(v)

2

Question 5

5.

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

(i)

3
(ii)

2
(iii)

1
(iv)

(-1)
(v)

4

Question 6

6.

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

(i)

4
(ii)

2
(iii)

5
(iv)

1
(v)

3

Question 7

7.

In the given figure, O is the centre of the circle and MN is the tangent at L. If ∠KIL = 47° and ∠IKJ = 62°, find ∠KIJ

(i)

38°
(ii)

43°
(iii)

33°
(iv)

58°
(v)

28°

Question 8

8.

In the given figure, O is the centre of the circle and FG is the tangent at C. If ∠ODC = 39°, find ∠GCD

(i)

61°
(ii)

81°
(iii)

56°
(iv)

66°
(v)

51°

Question 9

9.

In the given figure, O is the centre of the circle and the tangents FI and HI meet at point I. If ∠GHF = 53°, find ∠FOH

(i)

121°
(ii)

106°
(iii)

136°
(iv)

111°
(v)

116°

Question 10

10.

In the given figure, O is the centre of the circle and the tangents DG and FG meet at point G. If ∠EFD = 57°, find ∠FGD

(i)

66°
(ii)

71°
(iii)

96°
(iv)

76°
(v)

81°

Question 11

11.

In the given figure, O is the centre of the circle and EG is the tangent at F. If ∠FGH = 49°,∠GFH = 34°, find ∠JFE

(i)

93°
(ii)

98°
(iii)

113°
(iv)

83°
(v)

88°

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)

64°
(ii)

74°
(iii)

59°
(iv)

69°
(v)

89°

Question 13

13.

In the given figure, O is the centre of the circle and DF is the tangent at E. If ∠EFG = 28°,∠FEG = 40°, find ∠HEG

(i)

102°
(ii)

82°
(iii)

77°
(iv)

72°
(v)

87°

Question 14

14.

In the given figure, JH and JI are tangent segments to the circle with centre O. Given ∠IJK = 24°, find ∠HIO

(i)

29°
(ii)

24°
(iii)

34°
(iv)

39°
(v)

54°

Question 15

15.

In the given figure, JH and JI are tangent segments to the circle with centre O. Given ∠IJK = 30°, find ∠HIK

(i)

40°
(ii)

45°
(iii)

60°
(iv)

30°
(v)

35°

Question 16

16.

O is the centre of the circle. DE and FE are tangents to the circle. If ∠FGD = 51°, find ∠DEF

(i)

78°
(ii)

108°
(iii)

93°
(iv)

83°
(v)

88°

Question 17

17.

In the given figure, HI and JK are parallel tangents to the circle with centre O. HK is another tangent meeting HI and JK at H and K. Find ∠HOK

(i)

105°
(ii)

120°
(iii)

95°
(iv)

100°
(v)

90°

Question 18

18.

In the given figure, EH is the common tangent to the two circles. EF & EG are also tangents. Given EF = 15 cm, find EG

(i)

15 cm
(ii)

16 cm
(iii)

17 cm
(iv)

13 cm
(v)

14 cm

Question 19

19.

GH is a line segment and J is its mid-point. Three semi-circles are drawn with GJ , JH and GH as diameters. I , K and J respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given GI = 5 cm

(i)

3.33 cm
(ii)

5.33 cm
(iii)

1.33 cm
(iv)

4.33 cm
(v)

2.33 cm

Question 20

20.

In the given figure, CS & DS are tangents to the circle with centre O. Given ∠C = 21°, find ∠S

(i)

52°
(ii)

42°
(iii)

47°
(iv)

57°
(v)

72°

Question 21

21.

In the given figure, GP & HP are tangents to the circle with centre O. Given OG = 12 cm and GH = 22 cm, find GP

(i)

26.52 cm
(ii)

25.52 cm
(iii)

29.52 cm
(iv)

28.52 cm
(v)

27.52 cm

Question 22

22.

In the given figure, AQ & BQ are tangents to the circle with centre O. Given ∠AOB = 127°, find ∠AQB

(i)

83°
(ii)

58°
(iii)

53°
(iv)

68°
(v)

63°

Assignment Key