EduSahara™ Assignment
Name : Cyclic Quadrilateral
Chapter : Circles
Grade : SSC Grade IX
License : Non Commercial Use
Question
1
1.
O is the centre of the circle. If ∠JOL = 69°, find ∠I
(i)
34.5°
(ii)
64.5°
(iii)
39.5°
(iv)
44.5°
(v)
49.5°
Question
2
2.
O is the centre of the circle. If ∠IKJ = 40° and ∠KIL = 32°, find t°, u°
(i)
58°, 50°
(ii)
50°, 58°
(iii)
68°, 60°
(iv)
48°, 50°
(v)
88°, 70°
Question
3
3.
O is the centre of the circle. If ∠HIJ = 117°, find ∠JOK
(i)
54°
(ii)
84°
(iii)
69°
(iv)
59°
(v)
64°
Question
4
4.
O is the centre of the circle and ∠JGI = 37°, find ∠GHI
(i)
137°
(ii)
142°
(iii)
132°
(iv)
157°
(v)
127°
Question
5
5.
O is the centre of the circle. If ∠HFI = 37° and ∠FHG = 12°, find ∠GFH
(i)
71°
(ii)
46°
(iii)
41°
(iv)
51°
(v)
56°
Question
6
6.
In the given figure, O is the centre of the circle and EH is a diameter. If ∠EHI = 65° and ∠FHG = 39°, find ∠HEG
(i)
26°
(ii)
41°
(iii)
36°
(iv)
31°
(v)
56°
Question
7
7.
In the given figure, O is the centre of the circle and chord JK is equal to chord KL and KN is a diameter. If ∠JNK = 23°, find ∠NML
(i)
118°
(ii)
113°
(iii)
123°
(iv)
128°
(v)
143°
Question
8
8.
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 = 26° and ∠JKL = 116°, find ∠HIJ
(i)
133°
(ii)
128°
(iii)
143°
(iv)
138°
(v)
158°
Question
9
9.
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 = 50° find ∠GHI
(i)
85°
(ii)
110°
(iii)
80°
(iv)
90°
(v)
95°
Question
10
10.
In the given figure, O is the centre of the circle , chord DG is equal to chord GF. If ∠DOE = 89° and ∠DGF = 116°, find ∠EFG
(i)
106.5°
(ii)
81.5°
(iii)
91.5°
(iv)
86.5°
(v)
76.5°
Question
11
11.
In the given figure, O is the centre of the circle. If ∠FOG = 90° and ∠GHJ = 75°, find ∠IFO
(i)
30°
(ii)
60°
(iii)
45°
(iv)
35°
(v)
40°
Question
12
12.
In the given figure, O is the centre of the circle. If ∠FOG = 76° and ∠GHJ = 106°, find ∠IFO
(i)
84°
(ii)
64°
(iii)
69°
(iv)
54°
(v)
59°
Question
13
13.
In the given figure, O is the centre of the circle. If ∠MKL = 60° and ∠IJM = 87°, find ∠KML
(i)
63°
(ii)
33°
(iii)
48°
(iv)
38°
(v)
43°
Question
14
14.
In the given figure, O is the centre of the circle. If ∠EFI = 93°, find ∠GHI
(i)
98°
(ii)
103°
(iii)
123°
(iv)
108°
(v)
93°
Question
15
15.
In the given figure, O is the centre of the circle. If ∠JKH = 71°, find ∠HIJ
(i)
139°
(ii)
119°
(iii)
114°
(iv)
124°
(v)
109°
Question
16
16.
In the given figure, O is the centre of the circle and EH is a diameter. If ∠GHD = 85° and ∠DEH = 66°, find ∠EFG
(i)
149°
(ii)
124°
(iii)
134°
(iv)
129°
(v)
119°
Question
17
17.
In the given figure, O is the centre of the circle and BE is a diameter. If ∠CDE = 134°, find ∠CAB
(i)
59°
(ii)
54°
(iii)
49°
(iv)
74°
(v)
44°
Question
18
18.
In the given figure, O is the centre of the circle. If ∠JKL = 122.5°, find ∠LOJ + ∠JIL
(i)
302.5°
(ii)
317.5°
(iii)
332.5°
(iv)
312.5°
(v)
307.5°
Question
19
19.
In the given figure, O is the centre of the circle. If ∠BCF = 109° and ∠CDE = 108°, find ∠DGE
(i)
47°
(ii)
67°
(iii)
42°
(iv)
37°
(v)
52°
Question
20
20.
In the given figure, O is the centre of the circle . If ∠FIG = 68° and ∠FEH = 69°, find ∠EJF
(i)
26°
(ii)
41°
(iii)
31°
(iv)
36°
(v)
56°
Question
21
21.
In the given figure, O is the centre and CG is a diameter of the circle and chord CD is equal to chord FG. If ∠DBF = 44°, find ∠FBG + ∠DEF
(i)
159°
(ii)
189°
(iii)
164°
(iv)
169°
(v)
174°
Question
22
22.
In the given figure, O is the centre of the circle. If ∠JHI = 58°, find reflex ∠IOG
(i)
254°
(ii)
249°
(iii)
259°
(iv)
274°
(v)
244°
Question
23
23.
In the given figure, a pentagon is inscribed in a circle with centre O. Given GH = HI = IJ and ∠GHI = 120°. Find ∠GFH
(i)
60°
(ii)
40°
(iii)
45°
(iv)
30°
(v)
35°
Question
24
24.
In the given figure, a pentagon is inscribed in a circle with centre O. Given EF = FG = GH and ∠EFG = 122°. Find ∠EDH
(i)
97°
(ii)
102°
(iii)
87°
(iv)
92°
(v)
117°
Question
25
25.
In the given figure, a pentagon is inscribed in a circle with centre O. Given BC = CD = DE and ∠BCD = 120°. Find ∠DOE
(i)
70°
(ii)
60°
(iii)
90°
(iv)
65°
(v)
75°
Question
26
26.
In the given figure, a hexagon is inscribed in a circle with centre O. Given GH = HI = IJ and ∠JKL = 135.05°. Find ∠GKL
(i)
60.05°
(ii)
50.05°
(iii)
75.05°
(iv)
55.05°
(v)
45.05°
Question
27
27.
In the given figure, a hexagon is inscribed in a circle with centre O. Given BC = CD = DE and ∠EFG = 137.23°. Find ∠GBC
(i)
102.77°
(ii)
117.77°
(iii)
132.77°
(iv)
107.77°
(v)
112.77°
Question
28
28.
In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 110° and ∠EAB = 100°. Find ∠ABC
(i)
125°
(ii)
120°
(iii)
110°
(iv)
115°
(v)
140°
Question
29
29.
In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 116° and ∠EAB = 114°. Find ∠CDE
(i)
108°
(ii)
103°
(iii)
128°
(iv)
98°
(v)
113°
Question
30
30.
In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 114° and ∠EAB = 115°. Find ∠AED
(i)
99°
(ii)
104°
(iii)
129°
(iv)
109°
(v)
114°
Question
31
31.
In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 109° and ∠EAB = 108°. Find ∠EAD
(i)
37°
(ii)
52°
(iii)
67°
(iv)
42°
(v)
47°
Question
32
32.
In the given figure, O is the centre of the circle. EF is a diameter of the circle and GH is equal to radius. Find ∠EIF
(i)
75°
(ii)
65°
(iii)
70°
(iv)
60°
(v)
90°
Question
33
33.
In the given figure, O is the centre of the circle. If ∠DGE = 80° and ∠DCF = 65°, find ∠CFE
(i)
50°
(ii)
35°
(iii)
40°
(iv)
65°
(v)
45°
Question
34
34.
Which of the following statements are true?
a)
A cyclic quadrilateral is a regular polygon.
b)
If a parallelogram is cyclic, it is a rectangle.
c)
If a trapezium is cyclic, it is a rectangle.
d)
If a kite is cyclic, it is a square.
e)
If a rhombus is cyclic, it is a square.
(i)
{c,e,b}
(ii)
{c,e}
(iii)
{d,a,b}
(iv)
{b,e}
(v)
{a,b}
Question
35
35.
Which of the following are cyclic quadrilaterals?
a)
trapezium
b)
square
c)
rhombus
d)
rectangle
e)
parallelogram
f)
triangle
(i)
{a,b}
(ii)
{a,d,b}
(iii)
{c,d}
(iv)
{b,d}
(v)
{e,f,b}
Question
36
36.
Which of the following statements are true?
a)
It is always possible to inscribe a circle in a regular polygon.
b)
If a circle can be inscribed in a quadrilateral, then it must be a square.
c)
If a circle can be inscribed in a quadrilateral, it must be a kite.
d)
It is always possible to inscribe a circle in a quadrilateral.
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)
{a,e}
(ii)
{c,e,a}
(iii)
{d,b,a}
(iv)
{b,a}
(v)
{c,e}
Question
37
37.
Which of the following statements are true?
a)
Angles in the opposite segments are supplementary.
b)
Angles in the opposite segments are complementary.
c)
Angles in the same segment are equal.
d)
Angles subtended by equal length arcs in two circles are equal.
(i)
{b,d,a}
(ii)
{b,a}
(iii)
{d,c}
(iv)
{a,c}
(v)
{b,c,a}
Question
38
38.
The opposite angles in a cyclic quadrilateral are
(i)
linear pair
(ii)
complementary
(iii)
supplementary
(iv)
equal
Question
39
39.
In the given figure, EFGH is cyclic quadrilateral. If ∠FGH = 91°, find ∠DEH
(i)
96°
(ii)
91°
(iii)
121°
(iv)
101°
(v)
106°
Question
40
40.
In the given figure, O is the centre of the circle. If ∠CDO = 8° and ∠OFC = 42°, find ∠DEF
(i)
135°
(ii)
130°
(iii)
160°
(iv)
145°
(v)
140°
Question
41
41.
In the given figure, O is the centre of the circle. If ∠JKO = 30° and ∠OMJ = 28°, find ∠KOM
(i)
126°
(ii)
131°
(iii)
121°
(iv)
146°
(v)
116°
Question
42
42.
In the given figure, JKLM is a cyclic quadrilateral. If ∠JLK = 39° and ∠LMK = 48°, find ∠JKL
(i)
103°
(ii)
108°
(iii)
123°
(iv)
98°
(v)
93°
Question
43
43.
In the given figure, IJKL is a cyclic quadrilateral. If ∠IKJ = 38° and ∠KLJ = 50°, find ∠ILK
(i)
98°
(ii)
88°
(iii)
118°
(iv)
103°
(v)
93°
Question
44
44.
In the given figure, BCDEFG is a regular hexagon. Find ∠BDC
(i)
40°
(ii)
45°
(iii)
30°
(iv)
60°
(v)
35°
Question
45
45.
In the given figure, EFGHIJ is a regular hexagon. Find ∠EHG
(i)
75°
(ii)
90°
(iii)
60°
(iv)
65°
(v)
70°
Question
46
46.
In the given figure, ABCD is a cyclic quadrilateral. If ∠ABD = 74° and ∠BCA = 47°, find ∠BCD
(i)
121°
(ii)
126°
(iii)
131°
(iv)
136°
(v)
151°
Question
47
47.
In the given figure, HI , IJ , JK and KL are chords and HK , IL are diameters passing through the centre O. If ∠HOI = 52°. Find ∠IJK
(i)
146°
(ii)
121°
(iii)
116°
(iv)
126°
(v)
131°
Question
48
48.
In the given figure, FGHIJK is a regular hexagon inscribed in a circle with centre O. Which of the following are true?
a)
∠GJH = 30°
b)
∠FHG = 60°
c)
∠KIH = 90°
d)
∠FOK = 60°
e)
∠GOI = 120°
(i)
{b,e,a}
(ii)
{b,c}
(iii)
{b,a}
(iv)
{a,c,d,e}
(v)
{b,d}
Question
49
49.
In the given figure, EFGHI is a regular pentagon . Find ∠EIG
(i)
82°
(ii)
87°
(iii)
72°
(iv)
77°
(v)
102°
Question
50
50.
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)
50° & 130°
(iii)
40° & 140°
(iv)
45° & 135°
(v)
30° & 150°
Question
51
51.
In the given figure, FGHJ is a cyclic quadrilateral where GH and GF are produced to I and E respectively. If ∠EFJ = 95°, find ∠IHJ
(i)
100°
(ii)
115°
(iii)
90°
(iv)
95°
(v)
85°
Question
52
52.
In the given figure, ∠F = 46° , ∠I = 55° and ∠J = 134°, find ∠IGH
(i)
60°
(ii)
55°
(iii)
65°
(iv)
85°
(v)
70°
Question
53
53.
Which of the following statements are true?
a)
A cyclic kite is a square.
b)
A cyclic parallelogram is a rhombus.
c)
A cyclic rhombus is a square.
d)
A cyclic trapezium is a rectangle.
e)
A cyclic parallelogram is a rectangle.
(i)
{d,a,c}
(ii)
{b,e}
(iii)
{c,e}
(iv)
{a,c}
(v)
{b,e,c}
Question
54
54.
Which of the following statements are true?
a)
An isosceles trapezium is cyclic.
b)
The exterior angle of a quadrilateral and its interior opposite angle are supplementary.
c)
A quadrilateral in which the diagonals are equal and bisect each other is cyclic.
d)
Either pair of opposite angles of a cyclic quadrilateral are supplementary.
e)
All parallelograms are cyclic.
(i)
{e,c}
(ii)
{b,a,c}
(iii)
{a,c,d}
(iv)
{b,a}
(v)
{b,e,d}
Question
55
55.
Which of the following are not cyclic quadrilaterals?
a)
kite
b)
rhombus
c)
rectangle
d)
isosceles trapezium
e)
square
(i)
{e,c,a}
(ii)
{d,b,a}
(iii)
{d,b}
(iv)
{c,a}
(v)
{a,b}
Question
56
56.
If ABCD is a cyclic quadrilateral and ∠A − ∠C = 66°, then ∠C
(i)
87°
(ii)
57°
(iii)
72°
(iv)
67°
(v)
62°
Question
57
57.
If JKLM is a cyclic parallelogram, then ∠M
(i)
90°
(ii)
95°
(iii)
105°
(iv)
100°
(v)
120°
Question
58
58.
In the given figure, which of the following angle pairs are equal?
(i)
{(h,j),(k,l),(m,i),(g,f)}
(ii)
{(h,i),(j,f),(g,k),(m,l)}
(iii)
{(f,k),(g,j),(h,m),(i,l)}
(iv)
{(l,k),(j,g),(h,m),(i,f)}
(v)
{(l,m),(i,h),(k,j),(g,f)}
Question
59
59.
GHIJKL is a hexagon inscribed in a circle. Given ∠GHI = 132° & ∠IJK = 126°, find ∠KLG
(i)
112°
(ii)
102°
(iii)
132°
(iv)
107°
(v)
117°
Question
60
60.
In the given figure, IJKL is a parallelogram. The circumcircle of △IJK cuts KL at M. Given ∠ILM = 78°, find ∠LIM
(i)
24°
(ii)
34°
(iii)
29°
(iv)
54°
(v)
39°
Question
61
61.
In the given figure, HF and IE are two lines passing through the points of intersection of the two circles at G and D. If ∠IHG = 93° , find ∠GFE
(i)
92°
(ii)
102°
(iii)
87°
(iv)
117°
(v)
97°
Question
62
62.
In the given figure, find the angles of the quadrilateral.
(i)
A
=
112°
,
B
=
90°
,
C
=
68°
,
D
=
90°
(ii)
A
=
111°
,
B
=
90°
,
C
=
69°
,
D
=
90°
(iii)
A
=
108°
,
B
=
90°
,
C
=
72°
,
D
=
90°
(iv)
A
=
110°
,
B
=
90°
,
C
=
70°
,
D
=
90°
(v)
A
=
109°
,
B
=
90°
,
C
=
71°
,
D
=
90°
Question
63
63.
In the given figure, find the remaining angles of the quadrilateral.
(i)
D
=
106°
,
G
=
75°
(ii)
D
=
109°
,
G
=
78°
(iii)
D
=
107°
,
G
=
76°
(iv)
D
=
110°
,
G
=
79°
(v)
D
=
108°
,
G
=
77°
Question
64
64.
In the given figure, HI & IE are equal length chords, EG and FH are diameters. Given ∠IEO = 59° find, ∠FGO
(i)
33°
(ii)
43°
(iii)
28°
(iv)
58°
(v)
38°
Question
65
65.
In the given figure, ∠OGD = 40° & ∠OHG = 27°, find ∠FED
(i)
51°
(ii)
76°
(iii)
61°
(iv)
56°
(v)
46°
Assignment Key
1) (i)
2) (ii)
3) (i)
4) (v)
5) (iii)
6) (i)
7) (ii)
8) (ii)
9) (iii)
10) (v)
11) (i)
12) (iv)
13) (ii)
14) (v)
15) (v)
16) (v)
17) (v)
18) (i)
19) (iv)
20) (i)
21) (i)
22) (v)
23) (iv)
24) (iii)
25) (ii)
26) (v)
27) (i)
28) (iii)
29) (iv)
30) (i)
31) (i)
32) (iv)
33) (ii)
34) (iv)
35) (iv)
36) (i)
37) (iv)
38) (iii)
39) (ii)
40) (ii)
41) (v)
42) (v)
43) (ii)
44) (iii)
45) (iii)
46) (i)
47) (iii)
48) (iv)
49) (iii)
50) (v)
51) (v)
52) (ii)
53) (iii)
54) (iii)
55) (v)
56) (ii)
57) (i)
58) (iii)
59) (ii)
60) (i)
61) (iii)
62) (iv)
63) (v)
64) (iii)
65) (v)
