EduSahara™ Worksheet

Question 1

1.

The centre of the circle is

(i)

K
(ii)

M
(iii)

L
(iv)

O
(v)

J

Question 2

2.

The chords of the circle are

(i)

EF

,

FG

,

GH

,

HI

,

IE
(ii)

EF

,

FG

,

GH

,

HI

,

IE

,

GI
(iii)

FG

,

GH

,

HI

,

IE
(iv)

EF

,

FG

,

GH

,

HI

,

IE

,

JG
(v)

JE

,

JF

,

JG

,

JH

,

JI

Question 3

3.

The diameters of the circle are

(i)

MN

,

NO

,

OP

,

PQ

,

QR

,

RM

(ii)

SM

,

SN

,

SO

,

SP

,

SQ

,

SR

,

PR

(iii)

MN

,

NO

,

OP

,

PQ

,

QR

,

RM

,

PR

(iv)

PR
(v)

SM

,

SN

,

SO

,

SP

,

SQ

,

SR

Question 4

4.

The radii of the circle are

(i)

DE

,

EF

,

FG

,

GH

,

HD

,

ID
(ii)

DE

,

EF

,

FG

,

GH

,

HD

,

FH
(iii)

DE

,

EF

,

FG

,

GH

,

HD
(iv)

ID

,

IE

,

IF

,

IG

,

IH
(v)

EF

,

FG

,

GH

,

HD

Question 5

5.

The minor sector of the circle is

(i)

FIG
(ii)

KFHGK
(iii)

FHG
(iv)

FHGJF
(v)

FIGJF

Question 6

6.

The major sector of the circle is

(i)

BECFB
(ii)

GBDCG
(iii)

GBECG
(iv)

BDCFB
(v)

BEC

Question 7

7.

The minor arc of the circle is

(i)

CEDGC
(ii)

CFDGC
(iii)

CED
(iv)

CFD
(v)

HCEDH

Question 8

8.

The major arc of the circle is

(i)

LGIHL
(ii)

GJHKG
(iii)

GIH
(iv)

GJH
(v)

GIHKG

Question 9

9.

The minor segment of the circle is

(i)

ACBEA
(ii)

ACB
(iii)

ADBEA
(iv)

ADB
(v)

FACBF

Question 10

10.

The major segment of the circle is

(i)

HCEDH
(ii)

CED
(iii)

CFDGC
(iv)

HCFDH
(v)

CFD

Question 11

11.

The distance around the circle is called

(i)

chord
(ii)

diameter
(iii)

arc
(iv)

radius
(v)

circumference

Question 12

12.

'O' is the centre of a circle of radius 'r' and 'P' is any point in its plane.
If
OP
= r ,then P is

(i)

outside the circle
(ii)

on the circle
(iii)

inside the circle

Question 13

13.

'O' is the centre of a circle of radius 'r' and 'P' is any point in its plane.
If
OP
< r,then P is

(i)

on the circle
(ii)

outside the circle
(iii)

inside the circle

Question 14

14.

'O' is the centre of a circle of radius 'r' and 'P' is any point in its plane.
If
OP
> r,then P is

(i)

on the circle
(ii)

inside the circle
(iii)

outside the circle

Question 15

15.

The mid-point of the diameter of a circle is called

(i)

circumference
(ii)

centre
(iii)

diameter
(iv)

radius
(v)

chord

Question 16

16.

A line segment joining any point on the circle with its centre is called

(i)

semi-circle
(ii)

radius
(iii)

chord
(iv)

centre
(v)

major segment

Question 17

17.

A line segment having its end points on the circle is called a

(i)

centre
(ii)

semi-circle
(iii)

chord
(iv)

radius
(v)

diameter

Question 18

18.

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

(i)

chord
(ii)

diameter
(iii)

circumference
(iv)

segment
(v)

major segment

Question 19

19.

A chord of a circle divides the whole circular region into two parts, each called a

(i)

segment
(ii)

diameter
(iii)

semi-circle
(iv)

chord
(v)

radius

Question 20

20.

The segment of the circle containing the centre of the circle is called

(i)

diameter
(ii)

semi-circle
(iii)

centre
(iv)

segment
(v)

major segment

Question 21

21.

Half of a circle is called

(i)

semi-circle
(ii)

major segment
(iii)

radius
(iv)

chord
(v)

diameter

Question 22

22.

The perimeter of a circle is called

(i)

circumference
(ii)

segment
(iii)

diameter
(iv)

chord
(v)

semi-circle

Question 23

23.

Which of the following statements are true?

a)	Every circle has a unique centre.
b)	Every circle has a unique diameter.
c)	A circle consists of an infinite number of points.
d)	Each radius of a circle is also a chord of the circle.
e)	A line can meet a circle atmost at two points.

(i)

{b,d,e}
(ii)

{a,c,e}
(iii)

{d,c}
(iv)

{b,a}
(v)

{b,a,c}

Question 24

24.

Which of the following statements are true?

a)	Two semi-circles of a circle together make the whole circle.
b)	An infinite number of diameters may be drawn for a circle.
c)	One and only one tangent can be drawn to a circle from a point outside it.
d)	An infinite number of chords may be drawn for a circle.
e)	Every circle has a unique diameter.

(i)

{c,a,b}
(ii)

{e,b}
(iii)

{c,a}
(iv)

{a,b,d}
(v)

{c,e,d}

Question 25

25.

Which of the following statements are true?

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

(i)

{a,c}
(ii)

{e,a,c}
(iii)

{c,d}
(iv)

{b,d,c}
(v)

{b,d}

Question 26

26.

If the diameter of a circle is 112 cm, what is its radius?

(i)

55 cm
(ii)

54 cm
(iii)

58 cm
(iv)

56 cm
(v)

57 cm

Question 27

27.

If the radius of a circle is 84 cm, what is its diameter?

(i)

170 cm
(ii)

167 cm
(iii)

168 cm
(iv)

166 cm
(v)

169 cm

Question 28

28.

If the radius of a circle is 91 cm, what is its circumference?

(i)

572 cm
(ii)

570 cm
(iii)

574 cm
(iv)

571 cm
(v)

573 cm

Question 29

29.

In the given triangle S is the circumcentre. If SJ = 13.50 cm, find the circumference of the circumcircle

(i)

83.9 cm
(ii)

82.9 cm
(iii)

85.9 cm
(iv)

86.9 cm
(v)

84.9 cm

Question 30

30.

Two circles with equal radii are

(i)

concentric
(ii)

not similar
(iii)

congruent
(iv)

only similar but not congruent

Question 31

31.

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

(i)

secant
(ii)

semi-circle
(iii)

circumference
(iv)

major segment
(v)

tangent

Question 32

32.

A line which touches a circle at only one point is called a

(i)

major segment
(ii)

tangent
(iii)

segment
(iv)

radius
(v)

diameter

Question 33

33.

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)

radius
(ii)

chord
(iii)

semi-circle
(iv)

quadrant
(v)

tangent

Question 34

34.

Which of the following statements are true?

a)	A chord divides a circle into two segments.
b)	The diameter is the longest chord.
c)	The radius is the shortest chord.
d)	Atmost one chord can be drawn on a circle with a certain length.
e)	A chord divides a circle into two sectors.

(i)

{e,c,a}
(ii)

{d,b}
(iii)

{a,b}
(iv)

{c,a}
(v)

{d,b,a}

Question 35

35.

Which of the following statements are true?

a)	No two chords bisects each other.
b)	The longest chord of the circle passes through the centre of the circle.
c)	Equal length chords subtend equal angles at the centre of the circle.
d)	The farther the chord is from the centre, the larger the angle it subtends at the centre.
e)	Equal length chords are equidistant from the centre of the circle.

(i)

{a,b}
(ii)

{a,b,c}
(iii)

{a,d,e}
(iv)

{d,c}
(v)

{b,c,e}

Question 36

36.

Which of the following statements are true?

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

(i)

{d,c}
(ii)

{a,b}
(iii)

{a,b,c}
(iv)

{b,c,e}
(v)

{a,d,e}

Question 37

37.

Which of the following statements are true?

a)	Two chords bisect each other.
b)	The midpoint of any diameter of a circle is its centre.
c)	The diameter divides the circle into two unequal parts.
d)	A sector is the area enclosed by two radii and a chord.
e)	The longest of all chords of a circle is called diameter.

(i)

{c,e}
(ii)

{d,a,b}
(iii)

{a,b}
(iv)

{b,e}
(v)

{c,e,b}

Question 38

38.

Which of the following statements are true?

a)	Only one circle can be drawn passing through two points.
b)	Exactly two tangents can be drawn parallel to a secant.
c)	Infinite circles can be drawn passing through three collinear points.
d)	Atmost one circle can be drawn passing through three non-collinear points.
e)	Only one circle can be drawn with a centre.

(i)

{a,b}
(ii)

{c,d,b}
(iii)

{b,d}
(iv)

{c,d}
(v)

{e,a,b}

Question 39

39.

Which of the following statements are true?

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

(i)

{a,b}
(ii)

{d,c}
(iii)

{e,a,b}
(iv)

{d,c,b}
(v)

{b,c}

Question 40

40.

Which of the following statements are true?

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

(i)

{e,c}
(ii)

{a,b}
(iii)

{b,c,d}
(iv)

{a,b,c}
(v)

{a,e,d}

Question 41

41.

The point of intersection of the angular bisectors of a triangle is

(i)

orthocentre
(ii)

centroid
(iii)

excentre
(iv)

incentre
(v)

circumcentre

Question 42

42.

The angle subtended by the semicircle at the centre is

(i)

195°
(ii)

185°
(iii)

180°
(iv)

190°
(v)

210°

Question 43

43.

The angle subtended by the diameter at any point on the circle is

(i)

120°
(ii)

100°
(iii)

90°
(iv)

95°
(v)

105°

Question 44

44.

If the radius of the circumcircle is half the length of a side of the triangle, then the triangle is

(i)

equilateral triangle
(ii)

right angle triangle
(iii)

acute angled triangle
(iv)

obtuse angled triangle

Question 45

45.

Circles having common centre are called

(i)

congruent circles
(ii)

intersecting circles
(iii)

similar circles
(iv)

concentric circles

Question 46

46.

If two circles are concentric, then

(i)

their centres are same
(ii)

their diameters are same
(iii)

their perimeters are same
(iv)

their radii are same

Question 47

47.

Which of the following figures represent a chord ?

(i)

fig II
(ii)

fig I
(iii)

fig V
(iv)

fig IV
(v)

fig III

Question 48

48.

Which of the following figures represent a diameter ?

(i)

fig II
(ii)

fig I
(iii)

fig V
(iv)

fig III
(v)

fig IV

Question 49

49.

Which of the following figures represent a secant ?

(i)

fig II
(ii)

fig V
(iii)

fig IV
(iv)

fig I
(v)

fig III

Question 50

50.

Which of the following figures represent a tangent ?

(i)

fig II
(ii)

fig IV
(iii)

fig I
(iv)

fig V
(v)

fig III

Question 51

51.

Which of the following statements are true?

a)

π
is a rational number.

b)

22
7
is a rational number.

c)

A circle divides the plane into three mutually disjoint sets of points.

d)

All chords of a circle are diameters.

e)

All diameters of a circle are chords.

(i)

{a,d,e}
(ii)

{b,c,e}
(iii)

{a,b,c}
(iv)

{a,b}
(v)

{d,c}

Question 52

52.

Points which lie on the circumference of the circle are called

(i)

Concurrent points
(ii)

Cyclic points
(iii)

Concyclic points
(iv)

Coincident points
(v)

Similar points

Question 53

53.

Find the missing angle in the following figure?

(i)

23°
(ii)

18°
(iii)

33°
(iv)

48°
(v)

28°

Question 54

54.

O is the centre of the circle. If ∠DFE = 35° and ∠FDG = 37°, find y°, z°

(i)

55°, 53°
(ii)

53°, 55°
(iii)

63°, 65°
(iv)

83°, 75°
(v)

43°, 55°

Question 55

55.

If a chord HI = 12 cm is drawn in a circle with radius OH = 12 cm, find its distance from the centre of the circle

(i)

11.39 cm
(ii)

10.39 cm
(iii)

12.39 cm
(iv)

9.39 cm
(v)

8.39 cm

Question 56

56.

Two circles touch internally. G is the centre of the bigger circle and lies on the smaller circle. If ∠DEF = 37°, find ∠D

(i)

68°
(ii)

83°
(iii)

63°
(iv)

58°
(v)

53°

Question 57

57.

'D' and 'E' are centres of circles of radii 2 cm and 9 cm such that DE = 17 cm and 'F' is the centre of the circle of radius 'r' cm which touches the above circles externally. If ∠DFE = 90°, find 'r'

(i)

8 cm
(ii)

6 cm
(iii)

7 cm
(iv)

5 cm
(v)

4 cm

Question 58

58.

With the vertices of a triangle △GHI as centres, three circles are drawn touching each other externally. If the sides of the triangle are 9 cm , 15 cm and 12 cm , find the radii of the circles

(i)

3 cm , 11 cm & 9 cm respectively
(ii)

3 cm , 6 cm & 9 cm respectively
(iii)

3 cm , 6 cm & 14 cm respectively
(iv)

8 cm , 6 cm & 9 cm respectively
(v)

8 cm , 11 cm & 14 cm respectively

Question 59

59.

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)

120°
(iii)

95°
(iv)

105°
(v)

100°

Question 60

60.

In the given figure, find the angles of the quadrilateral.

(i)
C

=

96°

,

D

=

90°

,

E

=

84°

,

F

=

90°
(ii)
C

=

95°

,

D

=

90°

,

E

=

85°

,

F

=

90°
(iii)
C

=

93°

,

D

=

90°

,

E

=

87°

,

F

=

90°
(iv)
C

=

92°

,

D

=

90°

,

E

=

88°

,

F

=

90°
(v)
C

=

94°

,

D

=

90°

,

E

=

86°

,

F

=

90°

Assignment Key