EduSahara™ Worksheet

Question 1

1.

In the given figure, FT & GT are tangents to the circle with centre O. Given OF = 10 cm and FG = 17 cm, find FT

(i)

18.14 cm
(ii)

17.14 cm
(iii)

16.14 cm
(iv)

15.14 cm
(v)

14.14 cm

Question 2

2.

In the given figure, O is the centre of the circle and JK is the tangent at F. If ∠FIH = 57°, find ∠FGH

(i)

128°
(ii)

133°
(iii)

138°
(iv)

153°
(v)

123°

Question 3

3.

If 'l' is the length of the tangent drawn to a circle with radius 'r' from point 'P' which is 'd' cm away from the centre, then

(i)

l

=

√

(

d

2

−

r

2

)
(ii)

d

=

√

(

l

2

+

r

2

)
(iii)

r

=

√

(

l

2

+

d

2

)
(iv)

d

=

√

(

l

2

−

r

2

)
(v)

l

=

√

(

d

2

+

r

2

)

Question 4

4.

O is the centre of the circumcircle of △HIJ. Tangents at H and J intersect at K. If ∠HKJ = 59.87°, find ∠JIH

(i)

90.06°
(ii)

65.06°
(iii)

75.06°
(iv)

70.06°
(v)

60.06°

Question 5

5.

If two circles of radii 15 cm and 4 cm touch internally, the distance between their centres is

(i)

10 cm
(ii)

11 cm
(iii)

9 cm
(iv)

13 cm
(v)

12 cm

Question 6

6.

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

(i)

1
(ii)

4
(iii)

2
(iv)

0
(v)

(-1)

Question 7

7.

If two circles of radii 8 cm and 2 cm touch externally, the distance between their centres is

(i)

11 cm
(ii)

10 cm
(iii)

8 cm
(iv)

9 cm
(v)

12 cm

Question 8

8.

In the given figure, O is the centre of the circle and HI is the tangent at G. If ∠GFE = 36°, find ∠IGE

(i)

51°
(ii)

36°
(iii)

66°
(iv)

46°
(v)

41°

Question 9

9.

O is the centre of the circle. AB and CB are tangents to the circle. If ∠CDA = 42.5°, find ∠ABC

(i)

110°
(ii)

125°
(iii)

105°
(iv)

100°
(v)

95°

Question 10

10.

In the given figure, O is the centre of the circle and DF is the tangent at E. If ∠CBE = 27°, find ∠CDE + ∠CED

(i)

78°
(ii)

68°
(iii)

93°
(iv)

63°
(v)

73°

Question 11

11.

In the given figure, IJKL is a cyclic quadrilateral such that KI bisects ∠LIJ and MN is the tangent at K. If ∠KIJ = 57°, find ∠MKJ

(i)

72°
(ii)

57°
(iii)

87°
(iv)

67°
(v)

62°

Question 12

12.

In the given figure, O is the centre of the circle and HJ is the tangent at I . If ∠GFI = 29°, find ∠GHI

(i)

62°
(ii)

32°
(iii)

47°
(iv)

42°
(v)

37°

Question 13

13.

In the given figure, O is the centre of the circle and FG is the tangent at C. If ∠DCE = 51° and ∠FCD = 96°, find ∠CED

(i)

75°
(ii)

55°
(iii)

60°
(iv)

50°
(v)

45°

Question 14

14.

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 15

15.

In the given figure, two circles intersect at points I & J. A tangent is drawn at point K. From the same point, two lines are drawn passing through points I & J. They meet the other end of the second circle at H & G. Given ∠K = 55°, find ∠GHI

(i)

55°
(ii)

85°
(iii)

60°
(iv)

65°
(v)

70°

Question 16

16.

Which of the following statements are true?

a)	A secant of a circle is a segment having its end points on the circle.
b)	Diameter of a circle is a part of the semi-circle of the circle.
c)	One and only one tangent can be drawn to pass through a point on a circle.
d)	Every circle has a unique diameter.
e)	One and only one tangent can be drawn to a circle from a point outside it.

(i)

{a,b}
(ii)

{e,a,b}
(iii)

{b,c}
(iv)

{d,c,b}
(v)

{d,c}

Question 17

17.

In the given figure, O is the centre of the circle and HI is the tangent at G. If ∠GEF = 57°, find ∠HGF

(i)

72°
(ii)

87°
(iii)

62°
(iv)

67°
(v)

57°

Question 18

18.

In the given figure, O is the centre of the circle and MN is the tangent at I. If ∠ILK = 44°, find ∠NIK

(i)

74°
(ii)

49°
(iii)

59°
(iv)

54°
(v)

44°

Question 19

19.

In the given figure, JH and JI are tangent segments to the circle with centre O. Given ∠IJK = 25°, find ∠HIO

(i)

40°
(ii)

35°
(iii)

55°
(iv)

25°
(v)

30°

Question 20

20.

In the given figure, O is the centre of the circle and the tangents EH and GH meet at point H. If ∠FGE = 58°, find ∠GHE

(i)

79°
(ii)

74°
(iii)

94°
(iv)

64°
(v)

69°

Question 21

21.

Which of the following statements are true?

a)	If two circles touch internally, the distance between their centres is the difference of their radii.
b)	If two circles touch externally, their centres and the point of contact form an isosceles triangle.
c)	If two circles touch externally, the distance between their centres is the sum of their radii.
d)	If two circles touch internally, the square of the distance between their centres is the difference of the squares of their radii.
e)	If two circles touch internally, their centres and the point of contact form a scalene triangle.
f)	If two circles touch externally, the square of the distance between their centres is the sum of the squares of their radii.

(i)

{b,a}
(ii)

{e,f,a}
(iii)

{b,c,a}
(iv)

{d,c}
(v)

{a,c}

Question 22

22.

If the two radii OP and OQ of a circle are at right angles to each other, then the sector OPQ is called a

(i)

quadrant
(ii)

segment
(iii)

diameter
(iv)

radius
(v)

major segment

Question 23

23.

Which of the following statements are true?

a)	A tangent is the limiting case of a secant.
b)	A radius is a limiting case of a diameter.
c)	A diameter is a limiting case of a chord.
d)	A secant and a chord are same.
e)	A secant has two end points.

(i)

{b,a}
(ii)

{e,b,a}
(iii)

{a,c}
(iv)

{d,c}
(v)

{d,c,a}

Question 24

24.

In the given figure, O is the centre of the circle and LM is the tangent at K. If ∠JHK = 36° and ∠HJI = 61°, find ∠LKJ

(i)

51°
(ii)

66°
(iii)

41°
(iv)

46°
(v)

36°

Question 25

25.

In the given figure, O is the centre of the circle and HI is the tangent at E. If ∠FEG = 40° and ∠HEF = 48°, find ∠GEI

(i)

107°
(ii)

122°
(iii)

102°
(iv)

97°
(v)

92°

Assignment Key