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)

90°
(iii)

120°
(iv)

100°
(v)

95°

Question 3

3.

If two circles of radii 11 cm and 4 cm touch externally, the distance between their centres is

(i)

13 cm
(ii)

16 cm
(iii)

15 cm
(iv)

17 cm
(v)

14 cm

Question 4

4.

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

(i)

4
(ii)

0
(iii)

(-1)
(iv)

2
(v)

1

Question 5

5.

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

(i)

(-1)
(ii)

3
(iii)

2
(iv)

1
(v)

4

Question 6

6.

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

(i)

6
(ii)

2
(iii)

3
(iv)

0
(v)

4

Question 7

7.

In the given figure, O is the centre of the circle and HI is the tangent at G. If ∠FDG = 59° and ∠DFE = 49°, find ∠FDE

(i)

46°
(ii)

41°
(iii)

71°
(iv)

56°
(v)

51°

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)

57°
(ii)

87°
(iii)

62°
(iv)

72°
(v)

67°

Question 9

9.

In the given figure, O is the centre of the circle and the tangents DG and FG meet at point G. If ∠EFD = 56°, find ∠DOF

(i)

112°
(ii)

142°
(iii)

127°
(iv)

117°
(v)

122°

Question 10

10.

In the given figure, O is the centre of the circle and the tangents EH and GH meet at point H. If ∠FGE = 49°, find ∠GHE

(i)

92°
(ii)

82°
(iii)

87°
(iv)

112°
(v)

97°

Question 11

11.

In the given figure, O is the centre of the circle and HJ is the tangent at I. If ∠IJK = 42°,∠JIK = 39°, find ∠MIH

(i)

96°
(ii)

91°
(iii)

86°
(iv)

111°
(v)

81°

Question 12

12.

In the given figure, GHIJ is a cyclic quadrilateral such that IG bisects ∠JGH and KL is the tangent at I. If ∠IGH = 52°, find ∠KIH

(i)

52°
(ii)

57°
(iii)

67°
(iv)

82°
(v)

62°

Question 13

13.

In the given figure, O is the centre of the circle and GI is the tangent at H. If ∠HIJ = 28°,∠IHJ = 40°, find ∠KHJ

(i)

102°
(ii)

82°
(iii)

72°
(iv)

77°
(v)

87°

Question 14

14.

In the given figure, HF and HG are tangent segments to the circle with centre O. Given ∠GHI = 34°, find ∠FGO

(i)

34°
(ii)

64°
(iii)

39°
(iv)

49°
(v)

44°

Question 15

15.

In the given figure, EC and ED are tangent segments to the circle with centre O. Given ∠DEF = 21°, find ∠CDF

(i)

44.5°
(ii)

64.5°
(iii)

39.5°
(iv)

49.5°
(v)

34.5°

Question 16

16.

O is the centre of the circle. EF and GF are tangents to the circle. If ∠GHE = 32°, find ∠EFG

(i)

121°
(ii)

146°
(iii)

126°
(iv)

131°
(v)

116°

Question 17

17.

In the given figure, EF and GH are parallel tangents to the circle with centre O. EH is another tangent meeting EF and GH at E and H. Find ∠EOH

(i)

90°
(ii)

95°
(iii)

105°
(iv)

100°
(v)

120°

Question 18

18.

In the given figure, IL is the common tangent to the two circles. IJ & IK are also tangents. Given IJ = 14 cm, find IK

(i)

15 cm
(ii)

13 cm
(iii)

12 cm
(iv)

16 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 = 6 cm

(i)

3.00 cm
(ii)

5.00 cm
(iii)

4.00 cm
(iv)

6.00 cm
(v)

2.00 cm

Question 20

20.

In the given figure, EQ & FQ are tangents to the circle with centre O. Given ∠Q = 48°, find ∠E

(i)

29°
(ii)

34°
(iii)

54°
(iv)

39°
(v)

24°

Question 21

21.

In the given figure, EQ & FQ are tangents to the circle with centre O. Given OE = 12 cm and EF = 21 cm, find EQ

(i)

21.69 cm
(ii)

23.69 cm
(iii)

19.69 cm
(iv)

22.69 cm
(v)

20.69 cm

Question 22

22.

In the given figure, FR & GR are tangents to the circle with centre O. Given ∠FOG = 120°, find ∠FRG

(i)

70°
(ii)

90°
(iii)

75°
(iv)

60°
(v)

65°

Assignment Key