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)

90°
(ii)

105°
(iii)

120°
(iv)

100°
(v)

95°

Question 3

3.

If two circles of radii 12 cm and 5 cm touch externally, the distance between their centres is

(i)

19 cm
(ii)

17 cm
(iii)

18 cm
(iv)

15 cm
(v)

16 cm

Question 4

4.

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

(i)

2
(ii)

(-1)
(iii)

3
(iv)

1
(v)

0

Question 5

5.

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

(i)

2
(ii)

1
(iii)

3
(iv)

5
(v)

(-1)

Question 6

6.

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

(i)

4
(ii)

3
(iii)

2
(iv)

5
(v)

1

Question 7

7.

In the given figure, O is the centre of the circle and IJ is the tangent at H. If ∠GEH = 50° and ∠EGF = 61°, find ∠GEF

(i)

34°
(ii)

44°
(iii)

29°
(iv)

39°
(v)

59°

Question 8

8.

In the given figure, O is the centre of the circle and FG is the tangent at C. If ∠ODC = 38.5°, find ∠GCD

(i)

51.5°
(ii)

66.5°
(iii)

56.5°
(iv)

61.5°
(v)

81.5°

Question 9

9.

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 ∠IOK

(i)

130°
(ii)

105°
(iii)

100°
(iv)

115°
(v)

110°

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 = 51°, find ∠FGD

(i)

108°
(ii)

83°
(iii)

88°
(iv)

93°
(v)

78°

Question 11

11.

In the given figure, O is the centre of the circle and IK is the tangent at J. If ∠JKL = 41°,∠KJL = 37°, find ∠NJI

(i)

93°
(ii)

108°
(iii)

88°
(iv)

83°
(v)

78°

Question 12

12.

In the given figure, EFGH is a cyclic quadrilateral such that GE bisects ∠HEF and IJ is the tangent at G. If ∠GEF = 57°, find ∠IGF

(i)

87°
(ii)

72°
(iii)

62°
(iv)

57°
(v)

67°

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 = 36°, find ∠JGI

(i)

101°
(ii)

71°
(iii)

76°
(iv)

81°
(v)

86°

Question 14

14.

In the given figure, KI and KJ are tangent segments to the circle with centre O. Given ∠JKL = 25°, find ∠IJO

(i)

40°
(ii)

30°
(iii)

25°
(iv)

35°
(v)

55°

Question 15

15.

In the given figure, JH and JI are tangent segments to the circle with centre O. Given ∠IJK = 26°, find ∠HIK

(i)

62°
(ii)

37°
(iii)

47°
(iv)

32°
(v)

42°

Question 16

16.

O is the centre of the circle. DE and FE are tangents to the circle. If ∠FGD = 35.5°, find ∠DEF

(i)

119°
(ii)

114°
(iii)

124°
(iv)

109°
(v)

139°

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)

120°
(iv)

105°
(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)

13 cm
(iii)

16 cm
(iv)

17 cm
(v)

14 cm

Question 19

19.

FG is a line segment and I is its mid-point. Three semi-circles are drawn with FI , IG and FG as diameters. H , J and I respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given FH = 6 cm

(i)

6.00 cm
(ii)

5.00 cm
(iii)

2.00 cm
(iv)

4.00 cm
(v)

3.00 cm

Question 20

20.

In the given figure, GR & HR are tangents to the circle with centre O. Given ∠R = 44°, find ∠G

(i)

32°
(ii)

52°
(iii)

22°
(iv)

27°
(v)

37°

Question 21

21.

In the given figure, DR & ER are tangents to the circle with centre O. Given OD = 13 cm and DE = 24 cm, find DR

(i)

30.20 cm
(ii)

33.20 cm
(iii)

32.20 cm
(iv)

29.20 cm
(v)

31.20 cm

Question 22

22.

In the given figure, FR & GR are tangents to the circle with centre O. Given ∠FRG = 60°, find ∠FOG

(i)

135°
(ii)

130°
(iii)

125°
(iv)

120°
(v)

150°

Assignment Key