EduSahara™ Worksheet

Question 1

1.

'H' and 'I' are centres of circles of radii 2 cm and 4 cm such that HI = 10 cm and 'J' is the centre of the circle of radius 'r' cm which touches the above circles externally. If ∠HJI = 90°, find 'r'

(i)

4 cm
(ii)

6 cm
(iii)

5 cm
(iv)

2 cm
(v)

3 cm

Question 2

2.

The chords of the circle are

(i)

JK

,

KL

,

LM

,

MI
(ii)

NI

,

NJ

,

NK

,

NL

,

NM

(iii)

IJ

,

JK

,

KL

,

LM

,

MI

,

NM

(iv)

IJ

,

JK

,

KL

,

LM

,

MI

,

KM
(v)

IJ

,

JK

,

KL

,

LM

,

MI

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)

d

=

√

(

l

2

+

r

2

)
(ii)

d

=

√

(

l

2

−

r

2

)
(iii)

l

=

√

(

d

2

−

r

2

)
(iv)

r

=

√

(

l

2

+

d

2

)
(v)

l

=

√

(

d

2

+

r

2

)

Question 4

4.

The centre of the circle is

(i)

E
(ii)

D
(iii)

F
(iv)

G
(v)

I

Question 5

5.

In the given figure, O is the centre of the circle and MN is the tangent at L. If ∠KIL = 53° and ∠IKJ = 47°, find ∠NLI

(i)

47°
(ii)

52°
(iii)

67°
(iv)

42°
(v)

37°

Question 6

6.

Which of the following statements are true?

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

(i)

{a,c,e}
(ii)

{b,d,e}
(iii)

{c,d}
(iv)

{a,b,d}
(v)

{a,b}

Question 7

7.

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

(i)

{c,d}
(ii)

{c,d,a}
(iii)

{a,d}
(iv)

{b,a}
(v)

{e,b,a}

Question 8

8.

A chord that passes through the centre of the circle is called

(i)

radius
(ii)

semi-circle
(iii)

segment
(iv)

major segment
(v)

diameter

Question 9

9.

In the given triangle S is the circumcentre. If SF = 12.30 cm, find the circumference of the circumcircle

(i)

75.3 cm
(ii)

78.3 cm
(iii)

79.3 cm
(iv)

76.3 cm
(v)

77.3 cm

Question 10

10.

In the given figure, O is the centre of the circle. I is a point on chord GH such that GI = IH. Find ∠OIG

(i)

90°
(ii)

95°
(iii)

100°
(iv)

105°
(v)

120°

Question 11

11.

Find the area of the shaded region

(i)

181.93 sq.cm
(ii)

168.93 sq.cm
(iii)

152.93 sq.cm
(iv)

184.93 sq.cm
(v)

160.93 sq.cm

Question 12

12.

In the given figure, BC = 9 cm and AB = 13 cm. Find the area of the shaded region

(i)

144.93 sq.cm
(ii)

164.93 sq.cm
(iii)

122.93 sq.cm
(iv)

137.93 sq.cm
(v)

133.93 sq.cm

Question 13

13.

Which of the following statements are true?

a)	The area enclosed by a chord and its major arc is called major segment.
b)	A circle divides the plane on which it lies into three parts.
c)	The diameter divides the circle into two unequal parts.
d)	The area enclosed by a chord and its minor arc is called minor segment.
e)	A sector is the area enclosed by two radii and a chord.

(i)

{c,a}
(ii)

{c,e,d}
(iii)

{a,b,d}
(iv)

{c,a,b}
(v)

{e,b}

Question 14

14.

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

(i)

circumference
(ii)

quadrant
(iii)

centre
(iv)

secant
(v)

semi-circle

Question 15

15.

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

(i)

0
(ii)

3
(iii)

(-2)
(iv)

2
(v)

1

Question 16

16.

Circles having common centre are called

(i)

similar circles
(ii)

congruent circles
(iii)

concentric circles
(iv)

intersecting circles

Question 17

17.

In the given figure, the radius of the circle is 11 cm. Find the area of the major sector

(i)

313.21 sq.cm
(ii)

285.21 sq.cm
(iii)

267.21 sq.cm
(iv)

301.21 sq.cm
(v)

278.21 sq.cm

Question 18

18.

Which of the following figures represent a tangent ?

(i)

fig IV
(ii)

fig V
(iii)

fig I
(iv)

fig II
(v)

fig III

Question 19

19.

Half of a circle is called

(i)

chord
(ii)

radius
(iii)

segment
(iv)

semi-circle
(v)

diameter

Question 20

20.

In the given figure, the width of the circular path is 8.00 m. Find the area of the shaded region

(i)

889.14 sq.m
(ii)

1049.14 sq.m
(iii)

1199.14 sq.m
(iv)

869.14 sq.m
(v)

1219.14 sq.m

Question 21

21.

In the given figure, O is the centre of the circle and DF is the tangent at E . If ∠CBE = 30°, find ∠CDE

(i)

35°
(ii)

45°
(iii)

40°
(iv)

60°
(v)

30°

Question 22

22.

The major arc of the circle is

(i)

BEC
(ii)

BECFB
(iii)

GBECG
(iv)

BDC
(v)

BDCFB

Question 23

23.

In the given figure, IL is the common tangent to the two circles. IJ & IK are also tangents. Given IJ = 19 cm, find IK

(i)

19 cm
(ii)

18 cm
(iii)

17 cm
(iv)

20 cm
(v)

21 cm

Question 24

24.

The major sector of the circle is

(i)

KNLOK
(ii)

KML
(iii)

PKMLP
(iv)

KMLOK
(v)

PKNLP

Question 25

25.

If the diameter of a circle is 168 cm, what is its radius?

(i)

84 cm
(ii)

86 cm
(iii)

85 cm
(iv)

83 cm
(v)

82 cm

Assignment Key