EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Circles
Grade : SSC Grade IX
License : Non Commercial Use
Question
1
1.
An arc subtends 165° in its alternate segment. The arc is
(i)
minor arc
(ii)
major segment
(iii)
quadrant
(iv)
minor segment
(v)
major arc
Question
2
2.
O is the centre of the circle. If ∠CED = 60° and ∠ECF = 38°, find y°, z°
(i)
30°, 52°
(ii)
62°, 40°
(iii)
82°, 50°
(iv)
52°, 30°
(v)
42°, 30°
Question
3
3.
O is the centre of the circle. If ∠HIJ = 120°, find ∠JOK
(i)
70°
(ii)
60°
(iii)
90°
(iv)
75°
(v)
65°
Question
4
4.
In the given figure, JKLMN is a regular pentagon . Find ∠JNL
(i)
72°
(ii)
82°
(iii)
102°
(iv)
87°
(v)
77°
Question
5
5.
The radii of the circle are
(i)
ID
,
IE
,
IF
,
IG
,
IH
(ii)
EF
,
FG
,
GH
,
HD
(iii)
DE
,
EF
,
FG
,
GH
,
HD
,
IF
(iv)
DE
,
EF
,
FG
,
GH
,
HD
(v)
DE
,
EF
,
FG
,
GH
,
HD
,
FH
Question
6
6.
In the given figure, O is the centre of the circle. If ∠HIJ = 125°, find ∠JOH + ∠HGJ
(i)
310°
(ii)
335°
(iii)
315°
(iv)
305°
(v)
320°
Question
7
7.
Which of the following figures represent a secant ?
(i)
fig IV
(ii)
fig III
(iii)
fig I
(iv)
fig II
(v)
fig V
Question
8
8.
If the radius of a circle is 63 cm, what is its diameter?
(i)
125 cm
(ii)
126 cm
(iii)
127 cm
(iv)
128 cm
(v)
124 cm
Question
9
9.
The segment of the circle containing the centre of the circle is called
(i)
diameter
(ii)
circumference
(iii)
chord
(iv)
segment
(v)
major segment
Question
10
10.
Which of the following statements are true?
a)
A cyclic quadrilateral is a regular polygon.
b)
If a rhombus is cyclic, it is a square.
c)
If a trapezium is cyclic, it is a rectangle.
d)
If a kite is cyclic, it is a square.
e)
If a parallelogram is cyclic, it is a rectangle.
(i)
{c,e}
(ii)
{c,e,b}
(iii)
{a,b}
(iv)
{b,e}
(v)
{d,a,b}
Question
11
11.
The chords of the circle are
(i)
MH
,
MI
,
MJ
,
MK
,
ML
(ii)
HI
,
IJ
,
JK
,
KL
,
LH
,
JL
(iii)
IJ
,
JK
,
KL
,
LH
(iv)
HI
,
IJ
,
JK
,
KL
,
LH
,
MH
(v)
HI
,
IJ
,
JK
,
KL
,
LH
Question
12
12.
△LMN is inscribed in a circle with centre O. If ∠LOM = 105° and ∠MON = 164°, find ∠NLM
(i)
112°
(ii)
97°
(iii)
92°
(iv)
87°
(v)
82°
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)
inside the circle
(ii)
outside the circle
(iii)
on the circle
Question
14
14.
In the given figure, chords AC & BD meet at E. Given x = 106° and y = 38°, find ∠BAC
(i)
98°
(ii)
78°
(iii)
83°
(iv)
73°
(v)
68°
Question
15
15.
In the given figure, O is the centre of the circle. If ∠BOC = 73° and ∠CDF = 107°, find ∠EBO
(i)
53.5°
(ii)
58.5°
(iii)
68.5°
(iv)
63.5°
(v)
83.5°
Question
16
16.
In the given figure, O is the centre of the circle. Given ∠DOE = 41°, ∠COD = 37° and ∠EOF = 71°, find ∠CGF
(i)
104.5°
(ii)
89.5°
(iii)
84.5°
(iv)
79.5°
(v)
74.5°
Question
17
17.
In the given figure, two circles of radii JL = 8.6 cm & KL = 14.4 cm intersect at L & M. The distance between the centres JK = 20 cm, find the length of LM
(i)
12.87 cm
(ii)
9.87 cm
(iii)
10.87 cm
(iv)
8.87 cm
(v)
11.87 cm
Question
18
18.
If the diameter of a circle is 84 cm, what is its radius?
(i)
42 cm
(ii)
43 cm
(iii)
41 cm
(iv)
40 cm
(v)
44 cm
Question
19
19.
In the given figure, O is the centre of the circle. If ∠FGJ = 73°, find ∠HIJ
(i)
78°
(ii)
73°
(iii)
83°
(iv)
88°
(v)
103°
Question
20
20.
In the given figure, HJ is a chord which is equal to the radius of the circle. Find ∠K and ∠I
(i)
40° & 140°
(ii)
60° & 120°
(iii)
50° & 130°
(iv)
45° & 135°
(v)
30° & 150°
Question
21
21.
In the given figure, BCDE is a cyclic quadrilateral. If ∠BCE = 64° and ∠CDB = 48°, find ∠CDE
(i)
122°
(ii)
112°
(iii)
117°
(iv)
142°
(v)
127°
Question
22
22.
In the given figure, DE ∥ FG. Length of chords DE = 18 cm and FG = 28 cm.
If the distance between the chords is
8 cm
,
find the radius of the circle
(i)
16.36 cm
(ii)
13.36 cm
(iii)
15.36 cm
(iv)
12.36 cm
(v)
14.36 cm
Question
23
23.
In the given figure, △EAB is a scalene triangle. CA & DA trisect ∠EAB. Similarly BC & BD trisect ∠ABE. Given ∠BEA = 90°, find ∠BDA
(i)
130°
(ii)
125°
(iii)
135°
(iv)
150°
(v)
120°
Question
24
24.
In the given figure, ∠G = 40° , ∠J = 46° and ∠K = 137°, find ∠JHI
(i)
43°
(ii)
58°
(iii)
73°
(iv)
53°
(v)
48°
Question
25
25.
In the given figure, O is the centre of the circle. If ∠KIJ = 50° and ∠GHK = 91°, find ∠IKJ
(i)
69°
(ii)
44°
(iii)
39°
(iv)
54°
(v)
49°
Assignment Key
1) (v)
2) (i)
3) (ii)
4) (i)
5) (i)
6) (iv)
7) (v)
8) (ii)
9) (v)
10) (iv)
11) (v)
12) (v)
13) (i)
14) (v)
15) (i)
16) (v)
17) (iii)
18) (i)
19) (ii)
20) (v)
21) (ii)
22) (v)
23) (v)
24) (i)
25) (iii)