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)

95°
(ii)

105°
(iii)

90°
(iv)

100°
(v)

120°

Question 3

3.

If two circles of radii 11 cm and 7 cm touch externally, the distance between their centres is

(i)

18 cm
(ii)

16 cm
(iii)

20 cm
(iv)

19 cm
(v)

17 cm

Question 4

4.

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

(i)

1
(ii)

0
(iii)

(-2)
(iv)

2
(v)

4

Question 5

5.

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

(i)

2
(ii)

3
(iii)

(-1)
(iv)

1
(v)

5

Question 6

6.

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

(i)

5
(ii)

0
(iii)

3
(iv)

2
(v)

4

Question 7

7.

In the given figure, O is the centre of the circle and EF is the tangent at D. If ∠CAD = 55° and ∠ACB = 55°, find ∠CAB

(i)

65°
(ii)

45°
(iii)

40°
(iv)

50°
(v)

35°

Question 8

8.

In the given figure, O is the centre of the circle and FG is the tangent at C. If ∠ODC = 32°, find ∠GCD

(i)

58°
(ii)

73°
(iii)

63°
(iv)

88°
(v)

68°

Question 9

9.

In the given figure, O is the centre of the circle and the tangents HK and JK meet at point K. If ∠IJH = 55°, find ∠HOJ

(i)

115°
(ii)

125°
(iii)

140°
(iv)

110°
(v)

120°

Question 10

10.

In the given figure, O is the centre of the circle and the tangents GJ and IJ meet at point J. If ∠HIG = 51°, find ∠IJG

(i)

108°
(ii)

93°
(iii)

83°
(iv)

78°
(v)

88°

Question 11

11.

In the given figure, O is the centre of the circle and AC is the tangent at B. If ∠BCD = 45°,∠CBD = 35°, find ∠FBA

(i)

85°
(ii)

110°
(iii)

90°
(iv)

95°
(v)

80°

Question 12

12.

In the given figure, IJKL is a cyclic quadrilateral such that KI bisects ∠LIJ and MN is the tangent at K. If ∠KIJ = 53°, find ∠MKJ

(i)

53°
(ii)

63°
(iii)

83°
(iv)

68°
(v)

58°

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 = 34°, find ∠JGI

(i)

90°
(ii)

75°
(iii)

85°
(iv)

105°
(v)

80°

Question 14

14.

In the given figure, FD and FE are tangent segments to the circle with centre O. Given ∠EFG = 28°, find ∠DEO

(i)

43°
(ii)

38°
(iii)

28°
(iv)

58°
(v)

33°

Question 15

15.

In the given figure, JH and JI are tangent segments to the circle with centre O. Given ∠IJK = 32°, find ∠HIK

(i)

34°
(ii)

44°
(iii)

29°
(iv)

39°
(v)

59°

Question 16

16.

O is the centre of the circle. HI and JI are tangents to the circle. If ∠JKH = 41°, find ∠HIJ

(i)

108°
(ii)

128°
(iii)

113°
(iv)

98°
(v)

103°

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)

95°
(iii)

120°
(iv)

90°
(v)

100°

Question 18

18.

In the given figure, EH is the common tangent to the two circles. EF & EG are also tangents. Given EF = 19 cm, find EG

(i)

17 cm
(ii)

20 cm
(iii)

19 cm
(iv)

18 cm
(v)

21 cm

Question 19

19.

JK is a line segment and M is its mid-point. Three semi-circles are drawn with JM , MK and JK as diameters. L , N and M respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given JL = 6 cm

(i)

2.00 cm
(ii)

6.00 cm
(iii)

5.00 cm
(iv)

3.00 cm
(v)

4.00 cm

Question 20

20.

In the given figure, CQ & DQ are tangents to the circle with centre O. Given ∠Q = 48°, find ∠C

(i)

39°
(ii)

24°
(iii)

54°
(iv)

29°
(v)

34°

Question 21

21.

In the given figure, GQ & HQ are tangents to the circle with centre O. Given OG = 11 cm and GH = 19 cm, find GQ

(i)

19.84 cm
(ii)

16.84 cm
(iii)

18.84 cm
(iv)

20.84 cm
(v)

17.84 cm

Question 22

22.

In the given figure, CQ & DQ are tangents to the circle with centre O. Given ∠CQD = 61°, find ∠COD

(i)

134°
(ii)

119°
(iii)

124°
(iv)

149°
(v)

129°

Assignment Key