EduSahara™ Assignment
Name : Circle Concepts
Chapter : Tangents and Secants to a Circle
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
The centre of the circle is
(i)
I
(ii)
H
(iii)
K
(iv)
J
(v)
N
Question
2
2.
The chords of the circle are
(i)
LM
,
MN
,
NO
,
OP
,
PK
(ii)
QK
,
QL
,
QM
,
QN
,
QO
,
QP
(iii)
KL
,
LM
,
MN
,
NO
,
OP
,
PK
,
NP
(iv)
KL
,
LM
,
MN
,
NO
,
OP
,
PK
,
QK
(v)
KL
,
LM
,
MN
,
NO
,
OP
,
PK
Question
3
3.
The diameters of the circle are
(i)
PJ
,
PK
,
PL
,
PM
,
PN
,
PO
,
MO
(ii)
JK
,
KL
,
LM
,
MN
,
NO
,
OJ
(iii)
PJ
,
PK
,
PL
,
PM
,
PN
,
PO
(iv)
MO
(v)
JK
,
KL
,
LM
,
MN
,
NO
,
OJ
,
MO
Question
4
4.
The radii of the circle are
(i)
BC
,
CD
,
DE
,
EF
,
FB
,
DF
(ii)
CD
,
DE
,
EF
,
FB
(iii)
BC
,
CD
,
DE
,
EF
,
FB
(iv)
GB
,
GC
,
GD
,
GE
,
GF
(v)
BC
,
CD
,
DE
,
EF
,
FB
,
GD
Question
5
5.
The minor sector of the circle is
(i)
JLK
(ii)
JMKNJ
(iii)
JLKNJ
(iv)
OJLKO
(v)
JMK
Question
6
6.
The major sector of the circle is
(i)
DFEHD
(ii)
DGE
(iii)
DGEHD
(iv)
IDGEI
(v)
DFE
Question
7
7.
The minor arc of the circle is
(i)
ACBEA
(ii)
ACB
(iii)
FACBF
(iv)
ADBEA
(v)
FADBF
Question
8
8.
The major arc of the circle is
(i)
KFIGK
(ii)
FIGJF
(iii)
FHG
(iv)
FIG
(v)
FHGJF
Question
9
9.
The minor segment of the circle is
(i)
NIKJN
(ii)
NILJN
(iii)
ILJMI
(iv)
IKJMI
(v)
IKJ
Question
10
10.
The major segment of the circle is
(i)
IDGEI
(ii)
IDFEI
(iii)
DGE
(iv)
DFEHD
(v)
DGEHD
Question
11
11.
The distance around the circle is called
(i)
radius
(ii)
arc
(iii)
circumference
(iv)
chord
(v)
diameter
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)
on the circle
(ii)
outside 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)
inside the circle
(iii)
outside 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)
outside the circle
(ii)
inside the circle
(iii)
on the circle
Question
15
15.
The mid-point of the diameter of a circle is called
(i)
major segment
(ii)
segment
(iii)
chord
(iv)
centre
(v)
radius
Question
16
16.
A line segment joining any point on the circle with its centre is called
(i)
semi-circle
(ii)
diameter
(iii)
centre
(iv)
radius
(v)
segment
Question
17
17.
A line segment having its end points on the circle is called a
(i)
diameter
(ii)
centre
(iii)
major segment
(iv)
chord
(v)
radius
Question
18
18.
A chord that passes through the centre of the circle is called
(i)
centre
(ii)
diameter
(iii)
chord
(iv)
radius
(v)
semi-circle
Question
19
19.
A chord of a circle divides the whole circular region into two parts, each called a
(i)
diameter
(ii)
segment
(iii)
radius
(iv)
centre
(v)
major segment
Question
20
20.
The segment of the circle containing the centre of the circle is called
(i)
chord
(ii)
semi-circle
(iii)
major segment
(iv)
diameter
(v)
centre
Question
21
21.
Half of a circle is called
(i)
radius
(ii)
centre
(iii)
circumference
(iv)
major segment
(v)
semi-circle
Question
22
22.
The perimeter of a circle is called
(i)
circumference
(ii)
radius
(iii)
major segment
(iv)
semi-circle
(v)
chord
Question
23
23.
Which of the following statements are true?
a)
Every circle has a unique centre.
b)
A line can meet a circle atmost at two points.
c)
A circle consists of an infinite number of points.
d)
Every circle has a unique diameter.
e)
Each radius of a circle is also a chord of the circle.
(i)
{d,a,b}
(ii)
{a,b,c}
(iii)
{e,b}
(iv)
{d,a}
(v)
{d,e,c}
Question
24
24.
Which of the following statements are true?
a)
One and only one tangent can be drawn to a circle from a point outside it.
b)
An infinite number of diameters may be drawn for a circle.
c)
Every circle has a unique diameter.
d)
Two semi-circles of a circle together make the whole circle.
e)
An infinite number of chords may be drawn for a circle.
(i)
{b,d,e}
(ii)
{c,d}
(iii)
{a,c,e}
(iv)
{a,b}
(v)
{a,b,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)
Diameter of a circle is a part of the semi-circle of the circle.
d)
One and only one tangent can be drawn to pass through a point on a circle.
e)
One and only one tangent can be drawn to a circle from a point outside it.
(i)
{b,d,c}
(ii)
{b,d}
(iii)
{a,c}
(iv)
{e,a,c}
(v)
{c,d}
Question
26
26.
If the diameter of a circle is 56 cm, what is its radius?
(i)
29 cm
(ii)
30 cm
(iii)
27 cm
(iv)
28 cm
(v)
26 cm
Question
27
27.
If the radius of a circle is 56 cm, what is its diameter?
(i)
111 cm
(ii)
114 cm
(iii)
112 cm
(iv)
113 cm
(v)
110 cm
Question
28
28.
If the radius of a circle is 91 cm, what is its circumference?
(i)
573 cm
(ii)
571 cm
(iii)
572 cm
(iv)
574 cm
(v)
570 cm
Question
29
29.
In the given triangle S is the circumcentre. If SJ = 13.00 cm, find the circumference of the circumcircle
(i)
80.7 cm
(ii)
82.7 cm
(iii)
83.7 cm
(iv)
79.7 cm
(v)
81.7 cm
Question
30
30.
Two circles with equal radii are
(i)
congruent
(ii)
concentric
(iii)
not similar
(iv)
only similar but not congruent
Question
31
31.
A line which intersects the circle at two distinct points is called a
(i)
segment
(ii)
secant
(iii)
tangent
(iv)
circumference
(v)
quadrant
Question
32
32.
A line which touches a circle at only one point is called a
(i)
quadrant
(ii)
tangent
(iii)
segment
(iv)
circumference
(v)
major segment
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)
circumference
(ii)
secant
(iii)
tangent
(iv)
centre
(v)
quadrant
Question
34
34.
Which of the following statements are true?
a)
The radius is the shortest chord.
b)
The diameter is the longest chord.
c)
A chord divides a circle into two segments.
d)
A chord divides a circle into two sectors.
e)
Atmost one chord can be drawn on a circle with a certain length.
(i)
{a,b}
(ii)
{d,c,b}
(iii)
{e,a,b}
(iv)
{d,c}
(v)
{b,c}
Question
35
35.
Which of the following statements are true?
a)
The farther the chord is from the centre, the larger the angle it subtends at the centre.
b)
Equal length chords subtend equal angles at the centre of the circle.
c)
Equal length chords are equidistant from the centre of the circle.
d)
No two chords bisects each other.
e)
The longest chord of the circle passes through the centre of the circle.
(i)
{d,c}
(ii)
{a,b}
(iii)
{a,b,c}
(iv)
{a,d,e}
(v)
{b,c,e}
Question
36
36.
Which of the following statements are true?
a)
A circle divides the plane on which it lies into three parts.
b)
The diameter divides the circle into two unequal parts.
c)
The area enclosed by a chord and its major arc is called major segment.
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)
{b,e,d}
(ii)
{b,a}
(iii)
{a,c,d}
(iv)
{e,c}
(v)
{b,a,c}
Question
37
37.
Which of the following statements are true?
a)
The midpoint of any diameter of a circle is its centre.
b)
A sector is the area enclosed by two radii and a chord.
c)
The longest of all chords of a circle is called diameter.
d)
Two chords bisect each other.
e)
The diameter divides the circle into two unequal parts.
(i)
{d,c}
(ii)
{d,c,a}
(iii)
{a,c}
(iv)
{e,b,a}
(v)
{b,a}
Question
38
38.
Which of the following statements are true?
a)
Only one circle can be drawn with a centre.
b)
Atmost one circle can be drawn passing through three non-collinear points.
c)
Only one circle can be drawn passing through two points.
d)
Exactly two tangents can be drawn parallel to a secant.
e)
Infinite circles can be drawn passing through three collinear points.
(i)
{b,d}
(ii)
{c,d,b}
(iii)
{e,a,b}
(iv)
{a,b}
(v)
{c,d}
Question
39
39.
Which of the following statements are true?
a)
A radius is a limiting case of a diameter.
b)
A secant and a chord are same.
c)
A tangent is the limiting case of a secant.
d)
A diameter is a limiting case of a chord.
e)
A secant has two end points.
(i)
{b,d}
(ii)
{a,c}
(iii)
{c,d}
(iv)
{b,d,c}
(v)
{e,a,c}
Question
40
40.
Which of the following statements are true?
a)
The sides of a triangle can be tangents to a circle.
b)
Only two tangents can be drawn from a point outside the circle.
c)
Two tangents to a circle always intersect.
d)
Atmost one tangent can be drawn through a point inside the circle.
e)
Only one tangent can be drawn through a point on a circle.
(i)
{c,d,e}
(ii)
{d,b}
(iii)
{c,a}
(iv)
{a,b,e}
(v)
{c,a,b}
Question
41
41.
The point of intersection of the angular bisectors of a triangle is
(i)
orthocentre
(ii)
incentre
(iii)
excentre
(iv)
centroid
(v)
circumcentre
Question
42
42.
The angle subtended by the semicircle at the centre is
(i)
190°
(ii)
210°
(iii)
185°
(iv)
180°
(v)
195°
Question
43
43.
The angle subtended by the diameter at any point on the circle is
(i)
100°
(ii)
120°
(iii)
90°
(iv)
105°
(v)
95°
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)
concentric circles
(iii)
similar circles
(iv)
intersecting circles
Question
46
46.
If two circles are concentric, then
(i)
their radii are same
(ii)
their diameters are same
(iii)
their centres are same
(iv)
their perimeters are same
Question
47
47.
Which of the following figures represent a chord ?
(i)
fig II
(ii)
fig V
(iii)
fig III
(iv)
fig I
(v)
fig IV
Question
48
48.
Which of the following figures represent a diameter ?
(i)
fig V
(ii)
fig I
(iii)
fig III
(iv)
fig II
(v)
fig IV
Question
49
49.
Which of the following figures represent a secant ?
(i)
fig II
(ii)
fig III
(iii)
fig I
(iv)
fig IV
(v)
fig V
Question
50
50.
Which of the following figures represent a tangent ?
(i)
fig I
(ii)
fig V
(iii)
fig IV
(iv)
fig II
(v)
fig III
Question
51
51.
Which of the following statements are true?
a)
22
7
is a rational number.
b)
All chords of a circle are diameters.
c)
π
is a rational number.
d)
A circle divides the plane into three mutually disjoint sets of points.
e)
All diameters of a circle are chords.
(i)
{c,d}
(ii)
{a,d,e}
(iii)
{b,a}
(iv)
{b,c,e}
(v)
{b,a,d}
Question
52
52.
Points which lie on the circumference of the circle are called
(i)
Concyclic points
(ii)
Similar points
(iii)
Concurrent points
(iv)
Coincident points
(v)
Cyclic points
Question
53
53.
Find the missing angle in the following figure?
(i)
49°
(ii)
54°
(iii)
59°
(iv)
64°
(v)
79°
Question
54
54.
O is the centre of the circle. If ∠HJI = 59° and ∠JHK = 55°, find t°, u°
(i)
25°, 32°
(ii)
65°, 52°
(iii)
35°, 32°
(iv)
45°, 42°
(v)
32°, 35°
Question
55
55.
If a chord GH = 15 cm is drawn in a circle with radius OG = 10 cm, find its distance from the centre of the circle
(i)
5.61 cm
(ii)
6.61 cm
(iii)
7.61 cm
(iv)
8.61 cm
(v)
4.61 cm
Question
56
56.
Two circles touch internally. G is the centre of the bigger circle and lies on the smaller circle. If ∠DEF = 42°, find ∠D
(i)
53°
(ii)
78°
(iii)
58°
(iv)
48°
(v)
63°
Question
57
57.
'E' and 'F' are centres of circles of radii 4 cm and 11 cm such that EF = 17 cm and 'G' is the centre of the circle of radius 'r' cm which touches the above circles externally. If ∠EGF = 90°, find 'r'
(i)
6 cm
(ii)
3 cm
(iii)
5 cm
(iv)
4 cm
(v)
2 cm
Question
58
58.
With the vertices of a triangle △DEF as centres, three circles are drawn touching each other externally. If the sides of the triangle are 9 cm , 17 cm and 12 cm , find the radii of the circles
(i)
2 cm , 7 cm & 10 cm respectively
(ii)
7 cm , 12 cm & 15 cm respectively
(iii)
2 cm , 7 cm & 15 cm respectively
(iv)
2 cm , 12 cm & 10 cm respectively
(v)
7 cm , 7 cm & 10 cm respectively
Question
59
59.
In the given figure, O is the centre of the circle. J is a point on chord HI such that HJ = JI. Find ∠OJH
(i)
95°
(ii)
100°
(iii)
90°
(iv)
105°
(v)
120°
Question
60
60.
In the given figure, find the angles of the quadrilateral.
(i)
D
=
71°
,
E
=
90°
,
F
=
109°
,
G
=
90°
(ii)
D
=
73°
,
E
=
90°
,
F
=
107°
,
G
=
90°
(iii)
D
=
72°
,
E
=
90°
,
F
=
108°
,
G
=
90°
(iv)
D
=
74°
,
E
=
90°
,
F
=
106°
,
G
=
90°
(v)
D
=
70°
,
E
=
90°
,
F
=
110°
,
G
=
90°
Assignment Key
1) (v)
2) (v)
3) (iv)
4) (iv)
5) (iv)
6) (iv)
7) (ii)
8) (iv)
9) (iv)
10) (v)
11) (iii)
12) (i)
13) (ii)
14) (i)
15) (iv)
16) (iv)
17) (iv)
18) (ii)
19) (ii)
20) (iii)
21) (v)
22) (i)
23) (ii)
24) (i)
25) (v)
26) (iv)
27) (iii)
28) (iii)
29) (v)
30) (i)
31) (ii)
32) (ii)
33) (v)
34) (v)
35) (v)
36) (iii)
37) (iii)
38) (i)
39) (iii)
40) (iv)
41) (ii)
42) (iv)
43) (iii)
44) (ii)
45) (ii)
46) (iii)
47) (ii)
48) (v)
49) (ii)
50) (i)
51) (ii)
52) (i)
53) (i)
54) (v)
55) (ii)
56) (iv)
57) (iv)
58) (i)
59) (iii)
60) (iii)
