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)

120°
(iii)

95°
(iv)

105°
(v)

90°

Question 3

3.

If two circles of radii 15 cm and 6 cm touch externally, the distance between their centres is

(i)

19 cm
(ii)

20 cm
(iii)

23 cm
(iv)

22 cm
(v)

21 cm

Question 4

4.

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

(i)

2
(ii)

(-1)
(iii)

1
(iv)

4
(v)

0

Question 5

5.

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

(i)

5
(ii)

3
(iii)

0
(iv)

2
(v)

1

Question 6

6.

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

(i)

2
(ii)

0
(iii)

5
(iv)

3
(v)

4

Question 7

7.

In the given figure, O is the centre of the circle and JK is the tangent at I. If ∠HFI = 56° and ∠FHG = 46°, find ∠HFG

(i)

49°
(ii)

44°
(iii)

59°
(iv)

54°
(v)

74°

Question 8

8.

In the given figure, O is the centre of the circle and KL is the tangent at H. If ∠OIH = 39.5°, find ∠LHI

(i)

50.5°
(ii)

65.5°
(iii)

80.5°
(iv)

55.5°
(v)

60.5°

Question 9

9.

In the given figure, O is the centre of the circle and the tangents BE and DE meet at point E. If ∠CDB = 60°, find ∠BOD

(i)

135°
(ii)

125°
(iii)

130°
(iv)

150°
(v)

120°

Question 10

10.

In the given figure, O is the centre of the circle and the tangents HK and JK meet at point K. If ∠IJH = 56°, find ∠JKH

(i)

83°
(ii)

73°
(iii)

98°
(iv)

68°
(v)

78°

Question 11

11.

In the given figure, O is the centre of the circle and HJ is the tangent at I. If ∠IJK = 34°,∠JIK = 38°, find ∠MIH

(i)

82°
(ii)

77°
(iii)

87°
(iv)

102°
(v)

72°

Question 12

12.

In the given figure, ABCD is a cyclic quadrilateral such that CA bisects ∠DAB and EF is the tangent at C. If ∠CAB = 57°, find ∠ECB

(i)

62°
(ii)

67°
(iii)

87°
(iv)

57°
(v)

72°

Question 13

13.

In the given figure, O is the centre of the circle and FH is the tangent at G. If ∠GHI = 50°,∠HGI = 30°, find ∠JGI

(i)

75°
(ii)

70°
(iii)

85°
(iv)

80°
(v)

100°

Question 14

14.

In the given figure, KI and KJ are tangent segments to the circle with centre O. Given ∠JKL = 30°, find ∠IJO

(i)

45°
(ii)

60°
(iii)

40°
(iv)

35°
(v)

30°

Question 15

15.

In the given figure, EC and ED are tangent segments to the circle with centre O. Given ∠DEF = 33°, find ∠CDF

(i)

38.5°
(ii)

58.5°
(iii)

43.5°
(iv)

33.5°
(v)

28.5°

Question 16

16.

O is the centre of the circle. DE and FE are tangents to the circle. If ∠FGD = 49°, find ∠DEF

(i)

112°
(ii)

92°
(iii)

87°
(iv)

97°
(v)

82°

Question 17

17.

In the given figure, CD and EF are parallel tangents to the circle with centre O. CF is another tangent meeting CD and EF at C and F. Find ∠COF

(i)

90°
(ii)

120°
(iii)

95°
(iv)

105°
(v)

100°

Question 18

18.

In the given figure, CF is the common tangent to the two circles. CD & CE are also tangents. Given CD = 12 cm, find CE

(i)

10 cm
(ii)

13 cm
(iii)

12 cm
(iv)

14 cm
(v)

11 cm

Question 19

19.

DE is a line segment and G is its mid-point. Three semi-circles are drawn with DG , GE and DE as diameters. F , H and G respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given DF = 8 cm

(i)

7.33 cm
(ii)

4.33 cm
(iii)

3.33 cm
(iv)

6.33 cm
(v)

5.33 cm

Question 20

20.

In the given figure, BR & CR are tangents to the circle with centre O. Given ∠R = 42°, find ∠B

(i)

31°
(ii)

36°
(iii)

51°
(iv)

21°
(v)

26°

Question 21

21.

In the given figure, CT & DT are tangents to the circle with centre O. Given OC = 11 cm and CD = 19 cm, find CT

(i)

16.84 cm
(ii)

19.84 cm
(iii)

20.84 cm
(iv)

17.84 cm
(v)

18.84 cm

Question 22

22.

In the given figure, AP & BP are tangents to the circle with centre O. Given ∠AOB = 133°, find ∠APB

(i)

57°
(ii)

52°
(iii)

62°
(iv)

47°
(v)

77°

Assignment Key