EduSahara™ Worksheet

Question 1

1.

In the given figure, KI and KJ are tangent segments to the circle with centre O. Given ∠JKL = 28°, find ∠IJO

(i)

38°
(ii)

58°
(iii)

33°
(iv)

43°
(v)

28°

Question 2

2.

O is the centre of the circle. HI and JI are tangents to the circle. If ∠JKH = 55°, find ∠HIJ

(i)

85°
(ii)

70°
(iii)

100°
(iv)

75°
(v)

80°

Question 3

3.

In the given figure, O is the centre of the circle and FG is the tangent at C. If ∠ECD = 57° and ∠DCG = 43°, find ∠EDC

(i)

85°
(ii)

110°
(iii)

80°
(iv)

95°
(v)

90°

Question 4

4.

In the given figure, O is the centre of the circle and DE is the tangent at C. If ∠CAB = 54°, find ∠DCB

(i)

69°
(ii)

54°
(iii)

84°
(iv)

59°
(v)

64°

Question 5

5.

In the given figure, HIJK is a cyclic quadrilateral such that JH bisects ∠KHI and LM is the tangent at J. If ∠JHI = 60°, find ∠LJI

(i)

70°
(ii)

90°
(iii)

75°
(iv)

60°
(v)

65°

Question 6

6.

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

(i)

125°
(ii)

135°
(iii)

155°
(iv)

140°
(v)

130°

Question 7

7.

In the given figure, GP & HP are tangents to the circle with centre O. Given ∠G = 27°, find ∠P

(i)

54°
(ii)

84°
(iii)

69°
(iv)

64°
(v)

59°

Question 8

8.

In the given figure, O is the centre of the circle and CE is the tangent at D. If ∠DEF = 51°,∠EDF = 34°, find ∠GDF

(i)

91°
(ii)

76°
(iii)

61°
(iv)

71°
(v)

66°

Question 9

9.

A line which intersects the circle at two distinct points is called a

(i)

secant
(ii)

semi-circle
(iii)

tangent
(iv)

circumference
(v)

segment

Question 10

10.

In the given figure, O is the centre of the circle and DE is the tangent at C. If ∠CBA = 43°, find ∠ECA

(i)

53°
(ii)

73°
(iii)

43°
(iv)

58°
(v)

48°

Question 11

11.

In the given figure, CR & DR are tangents to the circle with centre O. Given OC = 10 cm and CD = 17 cm, find CR

(i)

14.14 cm
(ii)

15.14 cm
(iii)

18.14 cm
(iv)

17.14 cm
(v)

16.14 cm

Question 12

12.

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)

semi-circle
(iii)

chord
(iv)

major segment
(v)

tangent

Question 13

13.

Which of the following statements are true?

a)	A line parallel to a tangent is a secant.
b)	If two tangents to a circle intersect, their points of contact with the circle together with their point of intersection form an isosceles triangle.
c)	Two different tangents can meet at a point on the circle.
d)	If two tangents are perpendicular, they form a right angled triangle with their points of contact with the circle and their point of intersection.
e)	If two tangents are parallel, the distance between them is equal to the diameter of the circle.

(i)

{b,d,e}
(ii)

{c,d}
(iii)

{a,b}
(iv)

{a,b,d}
(v)

{a,c,e}

Question 14

14.

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)

d

=

√

(

l

2

+

r

2

)
(ii)

l

=

√

(

d

2

−

r

2

)
(iii)

r

=

√

(

l

2

+

d

2

)
(iv)

d

=

√

(

l

2

−

r

2

)
(v)

l

=

√

(

d

2

+

r

2

)

Question 15

15.

In the given figure, O is the centre of the circle and LM is the tangent at H. If ∠HKJ = 53°, find ∠HIJ

(i)

137°
(ii)

132°
(iii)

157°
(iv)

127°
(v)

142°

Question 16

16.

In the given figure, O is the centre of the circle and HJ is the tangent at I . If ∠GFI = 26°, find ∠GHI

(i)

68°
(ii)

53°
(iii)

48°
(iv)

43°
(v)

38°

Question 17

17.

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

(i)

2
(ii)

0
(iii)

3
(iv)

1
(v)

(-2)

Question 18

18.

In the given figure, FI is the common tangent to the two circles. FG & FH are also tangents. Given FG = 18 cm, find FH

(i)

20 cm
(ii)

18 cm
(iii)

16 cm
(iv)

19 cm
(v)

17 cm

Question 19

19.

Which of the following statements are true?

a)	Atmost three common tangents can be drawn touching two circles which touch each other.
b)	Atmost one common tangent can be drawn for any two concentric circles.
c)	A maximum of four common tangents can be drawn touching any two circles.
d)	Atmost two common tangents can be drawn touching any two circles.

(i)

{d,c}
(ii)

{a,c}
(iii)

{b,a}
(iv)

{b,c,a}
(v)

{b,d,a}

Question 20

20.

Which of the following statements are true?

a)	Only two tangents can be drawn from a point outside the circle.
b)	Only one tangent can be drawn through a point on a circle.
c)	Atmost one tangent can be drawn through a point inside the circle.
d)	The sides of a triangle can be tangents to a circle.
e)	Two tangents to a circle always intersect.

(i)

{c,e,d}
(ii)

{c,a}
(iii)

{c,a,b}
(iv)

{e,b}
(v)

{a,b,d}

Question 21

21.

Which of the following statements are true?

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

(i)

{e,f,a}
(ii)

{c,a}
(iii)

{a,b}
(iv)

{d,b}
(v)

{c,b,a}

Question 22

22.

The angle between a tangent to a circle and the radius drawn at the point of contact is

(i)

90°
(ii)

100°
(iii)

120°
(iv)

95°
(v)

105°

Question 23

23.

If two circles of radii 15 cm and 2 cm touch externally, the distance between their centres is

(i)

15 cm
(ii)

18 cm
(iii)

19 cm
(iv)

17 cm
(v)

16 cm

Question 24

24.

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 = 59°, find ∠GHI

(i)

74°
(ii)

59°
(iii)

69°
(iv)

64°
(v)

89°

Question 25

25.

In the given figure, DP & EP are tangents to the circle with centre O. Given ∠DPE = 58°, find ∠DOE

(i)

122°
(ii)

132°
(iii)

127°
(iv)

137°
(v)

152°

Assignment Key