EduSahara™ Assignment
Name : Cyclic Quadrilateral
Chapter : Circles
Grade : CBSE Grade IX
License : Non Commercial Use
Question
1
1.
O is the centre of the circle. If ∠EOG = 68°, find ∠D
(i)
34°
(ii)
44°
(iii)
64°
(iv)
39°
(v)
49°
Question
2
2.
O is the centre of the circle. If ∠DEF = 125°, find ∠FOG
(i)
85°
(ii)
75°
(iii)
100°
(iv)
80°
(v)
70°
Question
3
3.
O is the centre of the circle and ∠IFH = 33°, find ∠FGH
(i)
128°
(ii)
153°
(iii)
138°
(iv)
123°
(v)
133°
Question
4
4.
O is the centre of the circle. If ∠KIL = 34° and ∠IKJ = 20°, find ∠JIK
(i)
41°
(ii)
51°
(iii)
66°
(iv)
36°
(v)
46°
Question
5
5.
In the given figure, O is the centre of the circle and FI is a diameter. If ∠FIJ = 65° and ∠GIH = 37°, find ∠IFH
(i)
28°
(ii)
33°
(iii)
43°
(iv)
58°
(v)
38°
Question
6
6.
In the given figure, O is the centre of the circle and chord BC is equal to chord CD and CF is a diameter. If ∠BFC = 26°, find ∠FED
(i)
116°
(ii)
146°
(iii)
121°
(iv)
131°
(v)
126°
Question
7
7.
In the given figure, O is the centre of the circle and chord HI is equal to chord IJ and IL is a diameter. If ∠LHO = 27° and ∠JKL = 117°, find ∠HIJ
(i)
136°
(ii)
156°
(iii)
126°
(iv)
141°
(v)
131°
Question
8
8.
In the given figure, O is the centre of the circle , chord GH is equal to chord HI and FH is a diameter. If ∠IFH = 49° find ∠GHI
(i)
92°
(ii)
82°
(iii)
112°
(iv)
87°
(v)
97°
Question
9
9.
In the given figure, O is the centre of the circle. If ∠JOK = 72° and ∠KLN = 77°, find ∠MJO
(i)
38°
(ii)
23°
(iii)
53°
(iv)
33°
(v)
28°
Question
10
10.
In the given figure, O is the centre of the circle. If ∠AOB = 73° and ∠BCE = 99°, find ∠DAO
(i)
45.5°
(ii)
55.5°
(iii)
50.5°
(iv)
60.5°
(v)
75.5°
Question
11
11.
In the given figure, O is the centre of the circle. If ∠HFG = 44° and ∠DEH = 87°, find ∠FHG
(i)
59°
(ii)
64°
(iii)
49°
(iv)
54°
(v)
79°
Question
12
12.
In the given figure, O is the centre of the circle. If ∠EFI = 87°, find ∠GHI
(i)
117°
(ii)
97°
(iii)
92°
(iv)
102°
(v)
87°
Question
13
13.
In the given figure, O is the centre of the circle. If ∠HIF = 79°, find ∠FGH
(i)
101°
(ii)
116°
(iii)
111°
(iv)
106°
(v)
131°
Question
14
14.
In the given figure, O is the centre of the circle and FI is a diameter. If ∠HIE = 99° and ∠EFI = 56°, find ∠FGH
(i)
120°
(ii)
125°
(iii)
115°
(iv)
130°
(v)
145°
Question
15
15.
In the given figure, O is the centre of the circle and CF is a diameter. If ∠DEF = 136°, find ∠DBC
(i)
46°
(ii)
56°
(iii)
61°
(iv)
76°
(v)
51°
Question
16
16.
In the given figure, O is the centre of the circle and JL is a diameter. If ∠IOL = 112° and ∠OLK = 62°, find ∠JKI + ∠KJL
(i)
77°
(ii)
72°
(iii)
62°
(iv)
92°
(v)
67°
Question
17
17.
In the given figure, O is the centre of the circle. If ∠DEF = 124°, find ∠FOD + ∠DCF
(i)
314°
(ii)
304°
(iii)
319°
(iv)
309°
(v)
334°
Question
18
18.
In the given figure, O is the centre of the circle. If ∠EFI = 113° and ∠FGH = 115°, find ∠GJH
(i)
78°
(ii)
53°
(iii)
58°
(iv)
48°
(v)
63°
Question
19
19.
In the given figure, O is the centre of the circle . If ∠FIG = 64° and ∠FEH = 71°, find ∠EJF
(i)
56°
(ii)
36°
(iii)
26°
(iv)
41°
(v)
31°
Question
20
20.
In the given figure, O is the centre and BF is a diameter of the circle and chord BC is equal to chord EF. If ∠CAE = 36°, find ∠EAF + ∠CDE
(i)
171°
(ii)
176°
(iii)
186°
(iv)
201°
(v)
181°
Question
21
21.
In the given figure, O is the centre of the circle and EG is the tangent at F. If ∠FGH = 49°,∠GFH = 30°, find ∠JFE
(i)
79°
(ii)
109°
(iii)
89°
(iv)
84°
(v)
94°
Question
22
22.
In the given figure, O is the centre of the circle. If ∠HFG = 54.5°, find reflex ∠GOE
(i)
266°
(ii)
256°
(iii)
281°
(iv)
261°
(v)
251°
Question
23
23.
In the given figure, a pentagon is inscribed in a circle with centre O. Given HI = IJ = JK and ∠HIJ = 118°. Find ∠HGI
(i)
41°
(ii)
31°
(iii)
46°
(iv)
61°
(v)
36°
Question
24
24.
In the given figure, a pentagon is inscribed in a circle with centre O. Given HI = IJ = JK and ∠HIJ = 126°. Find ∠HGK
(i)
91°
(ii)
111°
(iii)
86°
(iv)
96°
(v)
81°
Question
25
25.
In the given figure, a pentagon is inscribed in a circle with centre O. Given HI = IJ = JK and ∠HIJ = 130°. Find ∠JOK
(i)
55°
(ii)
60°
(iii)
65°
(iv)
80°
(v)
50°
Question
26
26.
In the given figure, a hexagon is inscribed in a circle with centre O. Given EF = FG = GH and ∠HIJ = 124.93°. Find ∠EIJ
(i)
49.92°
(ii)
39.92°
(iii)
44.92°
(iv)
34.92°
(v)
64.92°
Question
27
27.
In the given figure, a hexagon is inscribed in a circle with centre O. Given EF = FG = GH and ∠HIJ = 122.62°. Find ∠JEF
(i)
127.38°
(ii)
122.38°
(iii)
117.38°
(iv)
132.38°
(v)
147.38°
Question
28
28.
In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 104° and ∠EAB = 118°. Find ∠ABC
(i)
134°
(ii)
109°
(iii)
114°
(iv)
104°
(v)
119°
Question
29
29.
In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 119° and ∠EAB = 105°. Find ∠CDE
(i)
135.5°
(ii)
120.5°
(iii)
115.5°
(iv)
105.5°
(v)
110.5°
Question
30
30.
In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 104° and ∠EAB = 105°. Find ∠AED
(i)
144°
(ii)
129°
(iii)
124°
(iv)
114°
(v)
119°
Question
31
31.
In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 106° and ∠EAB = 112°. Find ∠EAD
(i)
43°
(ii)
38°
(iii)
68°
(iv)
53°
(v)
48°
Question
32
32.
In the given figure, O is the centre of the circle. GH is a diameter of the circle and IJ is equal to radius. Find ∠GKH
(i)
75°
(ii)
60°
(iii)
65°
(iv)
70°
(v)
90°
Question
33
33.
In the given figure, O is the centre of the circle. If ∠HKI = 77° and ∠HGJ = 67°, find ∠GJI
(i)
66°
(ii)
36°
(iii)
41°
(iv)
51°
(v)
46°
Question
34
34.
Which of the following statements are true?
a)
If a rhombus is cyclic, it is a square.
b)
If a kite is cyclic, it is a square.
c)
If a trapezium is cyclic, it is a rectangle.
d)
If a parallelogram is cyclic, it is a rectangle.
e)
A cyclic quadrilateral is a regular polygon.
(i)
{a,d}
(ii)
{e,b,a}
(iii)
{c,d,a}
(iv)
{b,a}
(v)
{c,d}
Question
35
35.
Which of the following are cyclic quadrilaterals?
a)
rhombus
b)
trapezium
c)
rectangle
d)
square
e)
parallelogram
f)
triangle
(i)
{c,d}
(ii)
{a,d,c}
(iii)
{b,d}
(iv)
{e,f,c}
(v)
{a,c}
Question
36
36.
Which of the following statements are true?
a)
If a circle can be inscribed in a quadrilateral, then it must be a square.
b)
It is always possible to inscribe a circle in a quadrilateral.
c)
It is always possible to inscribe a circle in a regular polygon.
d)
If a circle can be inscribed in a quadrilateral, it must be a kite.
e)
If a circle can be inscribed in a quadrilateral, the sum of the lengths of a pair of opposite sides is equal to the other pair.
(i)
{b,e,c}
(ii)
{d,a,c}
(iii)
{a,c}
(iv)
{b,e}
(v)
{c,e}
Question
37
37.
Which of the following statements are true?
a)
Angles subtended by equal length arcs in two circles are equal.
b)
Angles in the opposite segments are supplementary.
c)
Angles in the same segment are equal.
d)
Angles in the opposite segments are complementary.
(i)
{d,c}
(ii)
{a,b}
(iii)
{a,d,b}
(iv)
{a,c,b}
(v)
{b,c}
Question
38
38.
The opposite angles in a cyclic quadrilateral are
(i)
supplementary
(ii)
equal
(iii)
linear pair
(iv)
complementary
Question
39
39.
In the given figure, O is the centre of the circle. If ∠IJO = 25° and ∠OLI = 32°, find ∠JKL
(i)
123°
(ii)
153°
(iii)
128°
(iv)
138°
(v)
133°
Question
40
40.
In the given figure, O is the centre of the circle. If ∠EFO = 40° and ∠OHE = 18°, find ∠FOH
(i)
116°
(ii)
126°
(iii)
121°
(iv)
131°
(v)
146°
Question
41
41.
In the given figure, HIJK is a cyclic quadrilateral. If ∠HJI = 40° and ∠JKI = 45°, find ∠HIJ
(i)
105°
(ii)
100°
(iii)
125°
(iv)
95°
(v)
110°
Question
42
42.
In the given figure, CDEF is a cyclic quadrilateral. If ∠CED = 37° and ∠EFD = 48°, find ∠CFE
(i)
95°
(ii)
90°
(iii)
115°
(iv)
100°
(v)
85°
Question
43
43.
In the given figure, DEFGHI is a regular hexagon. Find ∠DFE
(i)
30°
(ii)
45°
(iii)
40°
(iv)
60°
(v)
35°
Question
44
44.
In the given figure, ABCDEF is a regular hexagon. Find ∠ADC
(i)
65°
(ii)
75°
(iii)
70°
(iv)
90°
(v)
60°
Question
45
45.
In the given figure, DEFG is a cyclic quadrilateral. If ∠DEG = 70° and ∠EFD = 42°, find ∠EFG
(i)
142°
(ii)
117°
(iii)
122°
(iv)
127°
(v)
112°
Question
46
46.
In the given figure, ∠HJK = 11° and ∠HLK = 32°, find ∠JHK
(i)
47°
(ii)
52°
(iii)
57°
(iv)
62°
(v)
77°
Question
47
47.
In the given figure, ∠ACD = 10° and ∠AED = 28°, find ∠BDA
(i)
80°
(ii)
90°
(iii)
85°
(iv)
95°
(v)
110°
Question
48
48.
In the given figure, DE , EF , FG and GH are chords and DG , EH are diameters passing through the centre O. If ∠DOE = 74°. Find ∠EFG
(i)
157°
(ii)
132°
(iii)
142°
(iv)
137°
(v)
127°
Question
49
49.
In the given figure, FGHIJK is a regular hexagon inscribed in a circle with centre O. Which of the following are true?
a)
∠KIH = 90°
b)
∠FHG = 60°
c)
∠FOK = 60°
d)
∠GJH = 30°
e)
∠GOI = 120°
(i)
{a,c,d,e}
(ii)
{b,c}
(iii)
{b,a}
(iv)
{b,e,a}
(v)
{b,d}
Question
50
50.
In the given figure, EFGHI is a regular pentagon . Find ∠EIG
(i)
82°
(ii)
102°
(iii)
72°
(iv)
87°
(v)
77°
Question
51
51.
In the given figure, DF is a chord which is equal to the radius of the circle. Find ∠G and ∠E
(i)
60° & 120°
(ii)
45° & 135°
(iii)
30° & 150°
(iv)
50° & 130°
(v)
40° & 140°
Question
52
52.
In the given figure, EFGI is a cyclic quadrilateral where FG and FE are produced to H and D respectively. If ∠DEI = 83°, find ∠HGI
(i)
97°
(ii)
112°
(iii)
107°
(iv)
102°
(v)
127°
Question
53
53.
In the given figure, ∠G = 60° , ∠J = 58° and ∠K = 125°, find ∠JHI
(i)
73°
(ii)
78°
(iii)
63°
(iv)
93°
(v)
68°
Question
54
54.
Which of the following statements are true?
a)
A cyclic parallelogram is a rectangle.
b)
A cyclic parallelogram is a rhombus.
c)
A cyclic kite is a square.
d)
A cyclic rhombus is a square.
e)
A cyclic trapezium is a rectangle.
(i)
{b,a}
(ii)
{c,d,a}
(iii)
{c,d}
(iv)
{a,d}
(v)
{e,b,a}
Question
55
55.
Which of the following statements are true?
a)
A quadrilateral in which the diagonals are equal and bisect each other is cyclic.
b)
Either pair of opposite angles of a cyclic quadrilateral are supplementary.
c)
All parallelograms are cyclic.
d)
An isosceles trapezium is cyclic.
e)
The exterior angle of a quadrilateral and its interior opposite angle are supplementary.
(i)
{c,a}
(ii)
{a,b,d}
(iii)
{e,b}
(iv)
{c,e,d}
(v)
{c,a,b}
Question
56
56.
Which of the following are not cyclic quadrilaterals?
a)
rectangle
b)
rhombus
c)
square
d)
kite
e)
isosceles trapezium
(i)
{c,d}
(ii)
{c,d,b}
(iii)
{a,b}
(iv)
{b,d}
(v)
{e,a,b}
Question
57
57.
If JKLM is a cyclic quadrilateral and ∠J − ∠L = 74°, then ∠L
(i)
53°
(ii)
63°
(iii)
83°
(iv)
68°
(v)
58°
Question
58
58.
If DEFG is a cyclic parallelogram, then ∠G
(i)
100°
(ii)
95°
(iii)
90°
(iv)
120°
(v)
105°
Question
59
59.
DEFGHI is a hexagon inscribed in a circle. Given ∠DEF = 116° & ∠FGH = 130°, find ∠HID
(i)
114°
(ii)
124°
(iii)
129°
(iv)
119°
(v)
144°
Question
60
60.
In the given figure, ABCD is a parallelogram. The circumcircle of △ABC cuts CD at E. Given ∠ADE = 74°, find ∠DAE
(i)
42°
(ii)
47°
(iii)
37°
(iv)
32°
(v)
62°
Question
61
61.
In the given figure, KI and LH are two lines passing through the points of intersection of the two circles at J and G. If ∠LKJ = 99° , find ∠JIH
(i)
91°
(ii)
86°
(iii)
111°
(iv)
81°
(v)
96°
Question
62
62.
In the given figure, find the angles of the quadrilateral.
(i)
H
=
82°
,
I
=
90°
,
J
=
98°
,
K
=
90°
(ii)
H
=
81°
,
I
=
90°
,
J
=
99°
,
K
=
90°
(iii)
H
=
79°
,
I
=
90°
,
J
=
101°
,
K
=
90°
(iv)
H
=
78°
,
I
=
90°
,
J
=
102°
,
K
=
90°
(v)
H
=
80°
,
I
=
90°
,
J
=
100°
,
K
=
90°
Question
63
63.
In the given figure, find the remaining angles of the quadrilateral.
(i)
C
=
94°
,
D
=
95°
(ii)
C
=
92°
,
D
=
93°
(iii)
C
=
90°
,
D
=
91°
(iv)
C
=
91°
,
D
=
92°
(v)
C
=
93°
,
D
=
94°
Question
64
64.
In the given figure, ∠OEB = 50° & ∠DCB = 66°, find ∠OFE
(i)
22°
(ii)
17°
(iii)
12°
(iv)
7°
(v)
37°
Assignment Key
1) (i)
2) (v)
3) (iv)
4) (iv)
5) (i)
6) (i)
7) (iii)
8) (ii)
9) (ii)
10) (i)
11) (iii)
12) (v)
13) (i)
14) (iii)
15) (i)
16) (iii)
17) (ii)
18) (iv)
19) (iii)
20) (i)
21) (i)
22) (v)
23) (ii)
24) (v)
25) (v)
26) (iv)
27) (iii)
28) (iv)
29) (iv)
30) (iv)
31) (ii)
32) (ii)
33) (ii)
34) (i)
35) (i)
36) (v)
37) (v)
38) (i)
39) (i)
40) (i)
41) (iv)
42) (v)
43) (i)
44) (v)
45) (v)
46) (i)
47) (i)
48) (v)
49) (i)
50) (iii)
51) (iii)
52) (i)
53) (iii)
54) (iv)
55) (ii)
56) (iv)
57) (i)
58) (iii)
59) (i)
60) (iv)
61) (iv)
62) (v)
63) (ii)
64) (iv)
