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)

120°
(ii)

90°
(iii)

95°
(iv)

105°
(v)

100°

Question 3

3.

If two circles of radii 10 cm and 3 cm touch externally, the distance between their centres is

(i)

14 cm
(ii)

13 cm
(iii)

11 cm
(iv)

15 cm
(v)

12 cm

Question 4

4.

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

(i)

1
(ii)

(-2)
(iii)

0
(iv)

2
(v)

3

Question 5

5.

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

(i)

2
(ii)

0
(iii)

5
(iv)

3
(v)

1

Question 6

6.

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

(i)

3
(ii)

2
(iii)

6
(iv)

4
(v)

0

Question 7

7.

In the given figure, O is the centre of the circle and KL is the tangent at J. If ∠IGJ = 46° and ∠GIH = 61°, find ∠IGH

(i)

59°
(ii)

29°
(iii)

44°
(iv)

34°
(v)

39°

Question 8

8.

In the given figure, O is the centre of the circle and DE is the tangent at A. If ∠OBA = 31.5°, find ∠EAB

(i)

73.5°
(ii)

88.5°
(iii)

68.5°
(iv)

63.5°
(v)

58.5°

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 = 51°, find ∠FOH

(i)

107°
(ii)

132°
(iii)

102°
(iv)

117°
(v)

112°

Question 10

10.

In the given figure, O is the centre of the circle and the tangents BE and DE meet at point E. If ∠CDB = 49°, find ∠DEB

(i)

87°
(ii)

82°
(iii)

97°
(iv)

112°
(v)

92°

Question 11

11.

In the given figure, O is the centre of the circle and GI is the tangent at H. If ∠HIJ = 40°,∠IHJ = 37°, find ∠LHG

(i)

77°
(ii)

87°
(iii)

82°
(iv)

107°
(v)

92°

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 = 60°, find ∠KIH

(i)

65°
(ii)

90°
(iii)

75°
(iv)

60°
(v)

70°

Question 13

13.

In the given figure, O is the centre of the circle and AC is the tangent at B. If ∠BCD = 47°,∠CBD = 33°, find ∠EBD

(i)

67°
(ii)

72°
(iii)

97°
(iv)

82°
(v)

77°

Question 14

14.

In the given figure, GE and GF are tangent segments to the circle with centre O. Given ∠FGH = 32°, find ∠EFO

(i)

32°
(ii)

42°
(iii)

47°
(iv)

37°
(v)

62°

Question 15

15.

In the given figure, DB and DC are tangent segments to the circle with centre O. Given ∠CDE = 34°, find ∠BCE

(i)

28°
(ii)

33°
(iii)

43°
(iv)

58°
(v)

38°

Question 16

16.

O is the centre of the circle. IJ and KJ are tangents to the circle. If ∠KLI = 46.5°, find ∠IJK

(i)

102°
(ii)

97°
(iii)

87°
(iv)

117°
(v)

92°

Question 17

17.

In the given figure, FG and HI are parallel tangents to the circle with centre O. FI is another tangent meeting FG and HI at F and I. Find ∠FOI

(i)

90°
(ii)

95°
(iii)

100°
(iv)

120°
(v)

105°

Question 18

18.

In the given figure, IL is the common tangent to the two circles. IJ & IK are also tangents. Given IJ = 12 cm, find IK

(i)

12 cm
(ii)

11 cm
(iii)

13 cm
(iv)

10 cm
(v)

14 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 = 7 cm

(i)

3.67 cm
(ii)

2.67 cm
(iii)

5.67 cm
(iv)

4.67 cm
(v)

6.67 cm

Question 20

20.

In the given figure, DP & EP are tangents to the circle with centre O. Given ∠D = 30°, find ∠P

(i)

65°
(ii)

70°
(iii)

60°
(iv)

75°
(v)

90°

Question 21

21.

In the given figure, GP & HP are tangents to the circle with centre O. Given OG = 11 cm and GH = 20 cm, find GP

(i)

23.00 cm
(ii)

25.00 cm
(iii)

22.00 cm
(iv)

24.00 cm
(v)

26.00 cm

Question 22

22.

In the given figure, DT & ET are tangents to the circle with centre O. Given ∠DTE = 48°, find ∠DOE

(i)

162°
(ii)

147°
(iii)

142°
(iv)

132°
(v)

137°

Assignment Key