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 ∠HOJ = 103°, find ∠G
  • (i)
    61.5°
  • (ii)
    66.5°
  • (iii)
    56.5°
  • (iv)
    81.5°
  • (v)
    51.5°
Question 2
2.
O is the centre of the circle. If ∠CED = 53° and ∠ECF = 40°, find u°, v°
  • (i)
    60°, 47°
  • (ii)
    50°, 37°
  • (iii)
    37°, 50°
  • (iv)
    80°, 57°
  • (v)
    40°, 37°
Question 3
3.
O is the centre of the circle. If ∠FGH = 121°, find ∠HOI
  • (i)
    92°
  • (ii)
    72°
  • (iii)
    62°
  • (iv)
    77°
  • (v)
    67°
Question 4
4.
O is the centre of the circle and ∠GDF = 37°, find ∠DEF
  • (i)
    127°
  • (ii)
    132°
  • (iii)
    142°
  • (iv)
    137°
  • (v)
    157°
Question 5
5.
O is the centre of the circle. If ∠CAD = 34° and ∠ACB = 21°, find ∠BAC
  • (i)
    45°
  • (ii)
    65°
  • (iii)
    35°
  • (iv)
    40°
  • (v)
    50°
Question 6
6.
In the given figure, O is the centre of the circle and HK is a diameter. If ∠HKL = 60° and ∠IKJ = 31°, find ∠KHJ
  • (i)
    39°
  • (ii)
    29°
  • (iii)
    34°
  • (iv)
    59°
  • (v)
    44°
Question 7
7.
In the given figure, O is the centre of the circle and chord GH is equal to chord HI and HK is a diameter. If ∠GKH = 33°, find ∠KJI
  • (i)
    138°
  • (ii)
    153°
  • (iii)
    133°
  • (iv)
    128°
  • (v)
    123°
Question 8
8.
In the given figure, O is the centre of the circle and chord FG is equal to chord GH and GJ is a diameter. If ∠JFO = 25° and ∠HIJ = 115°, find ∠FGH
  • (i)
    140°
  • (ii)
    145°
  • (iii)
    135°
  • (iv)
    160°
  • (v)
    130°
Question 9
9.
In the given figure, O is the centre of the circle , chord HI is equal to chord IJ and GI is a diameter. If ∠JGI = 44° find ∠HIJ
  • (i)
    122°
  • (ii)
    107°
  • (iii)
    97°
  • (iv)
    102°
  • (v)
    92°
Question 10
10.
In the given figure, O is the centre of the circle , chord EH is equal to chord HG. If ∠EOF = 67° and ∠EHG = 99°, find ∠FGH
  • (i)
    104°
  • (ii)
    79°
  • (iii)
    84°
  • (iv)
    74°
  • (v)
    89°
Question 11
11.
In the given figure, O is the centre of the circle. If ∠HOI = 70° and ∠IJL = 102°, find ∠KHO
  • (i)
    47°
  • (ii)
    77°
  • (iii)
    52°
  • (iv)
    57°
  • (v)
    62°
Question 12
12.
In the given figure, O is the centre of the circle. If ∠EOF = 61° and ∠FGI = 106°, find ∠HEO
  • (i)
    76.5°
  • (ii)
    46.5°
  • (iii)
    56.5°
  • (iv)
    61.5°
  • (v)
    51.5°
Question 13
13.
In the given figure, O is the centre of the circle. If ∠LJK = 38° and ∠HIL = 98°, find ∠JLK
  • (i)
    54°
  • (ii)
    59°
  • (iii)
    44°
  • (iv)
    74°
  • (v)
    49°
Question 14
14.
In the given figure, O is the centre of the circle. If ∠JKN = 95°, find ∠LMN
  • (i)
    125°
  • (ii)
    110°
  • (iii)
    100°
  • (iv)
    95°
  • (v)
    105°
Question 15
15.
In the given figure, O is the centre of the circle. If ∠LMJ = 76°, find ∠JKL
  • (i)
    134°
  • (ii)
    104°
  • (iii)
    109°
  • (iv)
    119°
  • (v)
    114°
Question 16
16.
In the given figure, O is the centre of the circle and EH is a diameter. If ∠GHD = 96° and ∠DEH = 59°, find ∠EFG
  • (i)
    115°
  • (ii)
    125°
  • (iii)
    120°
  • (iv)
    130°
  • (v)
    145°
Question 17
17.
In the given figure, O is the centre of the circle and FI is a diameter. If ∠GHI = 140°, find ∠GEF
  • (i)
    50°
  • (ii)
    65°
  • (iii)
    60°
  • (iv)
    80°
  • (v)
    55°
Question 18
18.
In the given figure, O is the centre of the circle. If ∠HIJ = 120.5°, find ∠JOH + ∠HGJ
  • (i)
    310.5°
  • (ii)
    315.5°
  • (iii)
    300.5°
  • (iv)
    305.5°
  • (v)
    330.5°
Question 19
19.
In the given figure, O is the centre of the circle. If ∠EFI = 107° and ∠FGH = 109°, find ∠GJH
  • (i)
    36°
  • (ii)
    46°
  • (iii)
    41°
  • (iv)
    51°
  • (v)
    66°
Question 20
20.
In the given figure, O is the centre of the circle . If ∠GJH = 74° and ∠GFI = 68°, find ∠FKG
  • (i)
    35°
  • (ii)
    60°
  • (iii)
    45°
  • (iv)
    30°
  • (v)
    40°
Question 21
21.
In the given figure, O is the centre and EI is a diameter of the circle and chord EF is equal to chord HI. If ∠FDH = 34°, find ∠HDI + ∠FGH
  • (i)
    184°
  • (ii)
    189°
  • (iii)
    204°
  • (iv)
    179°
  • (v)
    174°
Question 22
22.
In the given figure, O is the centre of the circle. If ∠KIJ = 50.5°, find reflex ∠JOH
  • (i)
    269°
  • (ii)
    274°
  • (iii)
    289°
  • (iv)
    259°
  • (v)
    264°
Question 23
23.
In the given figure, a pentagon is inscribed in a circle with centre O. Given GH = HI = IJ and ∠GHI = 128°. Find ∠GFH
  • (i)
    56°
  • (ii)
    41°
  • (iii)
    36°
  • (iv)
    26°
  • (v)
    31°
Question 24
24.
In the given figure, a pentagon is inscribed in a circle with centre O. Given CD = DE = EF and ∠CDE = 106°. Find ∠CBF
  • (i)
    126°
  • (ii)
    116°
  • (iii)
    141°
  • (iv)
    121°
  • (v)
    111°
Question 25
25.
In the given figure, a pentagon is inscribed in a circle with centre O. Given DE = EF = FG and ∠DEF = 102°. Find ∠FOG
  • (i)
    93°
  • (ii)
    78°
  • (iii)
    108°
  • (iv)
    83°
  • (v)
    88°
Question 26
26.
In the given figure, a hexagon is inscribed in a circle with centre O. Given AB = BC = CD and ∠DEF = 134.79°. Find ∠AEF
  • (i)
    59.79°
  • (ii)
    74.79°
  • (iii)
    49.79°
  • (iv)
    44.79°
  • (v)
    54.79°
Question 27
27.
In the given figure, a hexagon is inscribed in a circle with centre O. Given HI = IJ = JK and ∠KLM = 132.38°. Find ∠MHI
  • (i)
    107.62°
  • (ii)
    117.62°
  • (iii)
    122.62°
  • (iv)
    137.62°
  • (v)
    112.62°
Question 28
28.
In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 108° and ∠EAB = 118°. Find ∠ABC
  • (i)
    138°
  • (ii)
    118°
  • (iii)
    108°
  • (iv)
    123°
  • (v)
    113°
Question 29
29.
In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 104° and ∠EAB = 114°. Find ∠CDE
  • (i)
    104°
  • (ii)
    109°
  • (iii)
    114°
  • (iv)
    119°
  • (v)
    134°
Question 30
30.
In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 102° and ∠EAB = 117°. Find ∠AED
  • (i)
    122°
  • (ii)
    117°
  • (iii)
    127°
  • (iv)
    132°
  • (v)
    147°
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 = 114°. Find ∠EAD
  • (i)
    45°
  • (ii)
    50°
  • (iii)
    70°
  • (iv)
    55°
  • (v)
    40°
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)
    90°
  • (ii)
    65°
  • (iii)
    60°
  • (iv)
    75°
  • (v)
    70°
Question 33
33.
In the given figure, O is the centre of the circle. If ∠FIG = 68° and ∠FEH = 70°, find ∠EHG
  • (i)
    72°
  • (ii)
    52°
  • (iii)
    47°
  • (iv)
    42°
  • (v)
    57°
Question 34
34.
Which of the following statements are true?
a)
A cyclic quadrilateral is a regular polygon.
b)
If a trapezium is cyclic, it is a rectangle.
c)
If a kite is cyclic, it is a square.
d)
If a rhombus is cyclic, it is a square.
e)
If a parallelogram is cyclic, it is a rectangle.
  • (i)
    {b,e,d}
  • (ii)
    {c,a,d}
  • (iii)
    {d,e}
  • (iv)
    {b,e}
  • (v)
    {a,d}
Question 35
35.
Which of the following are cyclic quadrilaterals?
a)
rhombus
b)
parallelogram
c)
triangle
d)
trapezium
e)
square
f)
rectangle
  • (i)
    {b,f}
  • (ii)
    {a,f,e}
  • (iii)
    {c,d,e}
  • (iv)
    {a,e}
  • (v)
    {e,f}
Question 36
36.
Which of the following statements are true?
a)
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.
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)
It is always possible to inscribe a circle in a regular polygon.
  • (i)
    {c,e,a}
  • (ii)
    {d,b,a}
  • (iii)
    {c,e}
  • (iv)
    {a,e}
  • (v)
    {b,a}
Question 37
37.
Which of the following statements are true?
a)
Angles in the opposite segments are supplementary.
b)
Angles subtended by equal length arcs in two circles are equal.
c)
Angles in the same segment are equal.
d)
Angles in the opposite segments are complementary.
  • (i)
    {a,c}
  • (ii)
    {b,a}
  • (iii)
    {b,c,a}
  • (iv)
    {d,c}
  • (v)
    {b,d,a}
Question 38
38.
The opposite angles in a cyclic quadrilateral are
  • (i)
    equal
  • (ii)
    linear pair
  • (iii)
    supplementary
  • (iv)
    complementary
Question 39
39.
In the given figure, KLMN is cyclic quadrilateral. If ∠LMN = 92°, find ∠JKN
  • (i)
    92°
  • (ii)
    122°
  • (iii)
    102°
  • (iv)
    97°
  • (v)
    107°
Question 40
40.
In the given figure, O is the centre of the circle. If ∠GHO = 51° and ∠OJG = 8°, find ∠HIJ
  • (i)
    126°
  • (ii)
    151°
  • (iii)
    131°
  • (iv)
    121°
  • (v)
    136°
Question 41
41.
In the given figure, O is the centre of the circle. If ∠IJO = 38° and ∠OLI = 21°, find ∠JOL
  • (i)
    133°
  • (ii)
    128°
  • (iii)
    123°
  • (iv)
    148°
  • (v)
    118°
Question 42
42.
In the given figure, ABCD is a cyclic quadrilateral. If ∠ACB = 36° and ∠CDB = 36°, find ∠ABC
  • (i)
    118°
  • (ii)
    123°
  • (iii)
    108°
  • (iv)
    138°
  • (v)
    113°
Question 43
43.
In the given figure, IJKL is a cyclic quadrilateral. If ∠IKJ = 30° and ∠KLJ = 38°, find ∠ILK
  • (i)
    78°
  • (ii)
    83°
  • (iii)
    68°
  • (iv)
    73°
  • (v)
    98°
Question 44
44.
In the given figure, HIJKLM is a regular hexagon. Find ∠HJI
  • (i)
    60°
  • (ii)
    45°
  • (iii)
    40°
  • (iv)
    35°
  • (v)
    30°
Question 45
45.
In the given figure, DEFGHI is a regular hexagon. Find ∠DGF
  • (i)
    60°
  • (ii)
    75°
  • (iii)
    70°
  • (iv)
    90°
  • (v)
    65°
Question 46
46.
In the given figure, BCDE is a cyclic quadrilateral. If ∠BCE = 67° and ∠CDB = 41°, find ∠EBC
  • (i)
    72°
  • (ii)
    82°
  • (iii)
    77°
  • (iv)
    102°
  • (v)
    87°
Question 47
47.
In the given figure, IJ , JK , KL and LM are chords and IL , JM are diameters passing through the centre O. If ∠IOJ = 77°. Find ∠JKL
  • (i)
    128.5°
  • (ii)
    143.5°
  • (iii)
    158.5°
  • (iv)
    133.5°
  • (v)
    138.5°
Question 48
48.
In the given figure, HIJKLM is a regular hexagon inscribed in a circle with centre O. Which of the following are true?
a)
    • ∠IOK = 120°
b)
    • ∠MKJ = 90°
c)
    • ∠HJI = 60°
d)
    • ∠ILJ = 30°
e)
    • ∠HOM = 60°
  • (i)
    {c,d}
  • (ii)
    {c,a}
  • (iii)
    {c,b}
  • (iv)
    {c,e,a}
  • (v)
    {a,b,d,e}
Question 49
49.
In the given figure, EFGHI is a regular pentagon . Find ∠EIG
  • (i)
    77°
  • (ii)
    82°
  • (iii)
    72°
  • (iv)
    87°
  • (v)
    102°
Question 50
50.
In the given figure, AC is a chord which is equal to the radius of the circle. Find ∠D and ∠B
  • (i)
    40° & 140°
  • (ii)
    60° & 120°
  • (iii)
    45° & 135°
  • (iv)
    30° & 150°
  • (v)
    50° & 130°
Question 51
51.
In the given figure, JKLN is a cyclic quadrilateral where KL and KJ are produced to M and I respectively. If ∠IJN = 95°, find ∠MLN
  • (i)
    85°
  • (ii)
    90°
  • (iii)
    115°
  • (iv)
    95°
  • (v)
    100°
Question 52
52.
In the given figure, ∠C = 63° , ∠F = 59° and ∠G = 131°, find ∠FDE
  • (i)
    83°
  • (ii)
    103°
  • (iii)
    88°
  • (iv)
    73°
  • (v)
    78°
Question 53
53.
Which of the following statements are true?
a)
A cyclic rhombus is a square.
b)
A cyclic parallelogram is a rectangle.
c)
A cyclic parallelogram is a rhombus.
d)
A cyclic kite is a square.
e)
A cyclic trapezium is a rectangle.
  • (i)
    {a,b}
  • (ii)
    {e,c,a}
  • (iii)
    {d,b}
  • (iv)
    {d,b,a}
  • (v)
    {c,a}
Question 54
54.
Which of the following statements are true?
a)
Either pair of opposite angles of a cyclic quadrilateral are supplementary.
b)
A quadrilateral in which the diagonals are equal and bisect each other is cyclic.
c)
An isosceles trapezium is cyclic.
d)
The exterior angle of a quadrilateral and its interior opposite angle are supplementary.
e)
All parallelograms are cyclic.
  • (i)
    {a,b,c}
  • (ii)
    {e,b}
  • (iii)
    {d,a}
  • (iv)
    {d,a,b}
  • (v)
    {d,e,c}
Question 55
55.
Which of the following are not cyclic quadrilaterals?
a)
rectangle
b)
square
c)
rhombus
d)
isosceles trapezium
e)
kite
  • (i)
    {b,e}
  • (ii)
    {c,e}
  • (iii)
    {b,e,c}
  • (iv)
    {d,a,c}
  • (v)
    {a,c}
Question 56
56.
If GHIJ is a cyclic quadrilateral and ∠G − ∠I = 12°, then ∠I
  • (i)
    89°
  • (ii)
    99°
  • (iii)
    94°
  • (iv)
    114°
  • (v)
    84°
Question 57
57.
If ABCD is a cyclic parallelogram, then ∠D
  • (i)
    105°
  • (ii)
    120°
  • (iii)
    90°
  • (iv)
    100°
  • (v)
    95°
Question 58
58.
In the given figure, which of the following angle pairs are equal?
  • (i)
    {(r,p),(u,t),(v,q),(w,s)}
  • (ii)
    {(v,q),(w,r),(p,s),(t,u)}
  • (iii)
    {(p,u),(q,t),(r,w),(s,v)}
  • (iv)
    {(r,w),(p,v),(u,t),(q,s)}
  • (v)
    {(w,p),(q,r),(u,t),(s,v)}
Question 59
59.
EFGHIJ is a hexagon inscribed in a circle. Given ∠EFG = 136° & ∠GHI = 129°, find ∠IJE
  • (i)
    110°
  • (ii)
    105°
  • (iii)
    125°
  • (iv)
    100°
  • (v)
    95°
Question 60
60.
In the given figure, ABCD is a parallelogram. The circumcircle of △ABC cuts CD at E. Given ∠ADE = 73°, find ∠DAE
  • (i)
    34°
  • (ii)
    44°
  • (iii)
    49°
  • (iv)
    39°
  • (v)
    64°
Question 61
61.
In the given figure, EC and FB are two lines passing through the points of intersection of the two circles at D and A. If ∠FED = 71° , find ∠DCB
  • (i)
    119°
  • (ii)
    114°
  • (iii)
    124°
  • (iv)
    139°
  • (v)
    109°
Question 62
62.
In the given figure, find the angles of the quadrilateral.
  • (i)
      • C
      • =
      • 100°
      • ,
      • D
      • =
      • 90°
      • ,
      • E
      • =
      • 80°
      • ,
      • F
      • =
      • 90°
  • (ii)
      • C
      • =
      • 97°
      • ,
      • D
      • =
      • 90°
      • ,
      • E
      • =
      • 83°
      • ,
      • F
      • =
      • 90°
  • (iii)
      • C
      • =
      • 101°
      • ,
      • D
      • =
      • 90°
      • ,
      • E
      • =
      • 79°
      • ,
      • F
      • =
      • 90°
  • (iv)
      • C
      • =
      • 99°
      • ,
      • D
      • =
      • 90°
      • ,
      • E
      • =
      • 81°
      • ,
      • F
      • =
      • 90°
  • (v)
      • C
      • =
      • 98°
      • ,
      • D
      • =
      • 90°
      • ,
      • E
      • =
      • 82°
      • ,
      • F
      • =
      • 90°
Question 63
63.
In the given figure, find the remaining angles of the quadrilateral.
  • (i)
    D
    =
    95°
    ,
    E
    =
    98°
  • (ii)
    D
    =
    93°
    ,
    E
    =
    96°
  • (iii)
    D
    =
    91°
    ,
    E
    =
    94°
  • (iv)
    D
    =
    94°
    ,
    E
    =
    97°
  • (v)
    D
    =
    92°
    ,
    E
    =
    95°
Question 64
64.
In the given figure, IJ & JF are equal length chords, FH and GI are diameters. Given ∠OIJ = 58° find, ∠HOG
  • (i)
    133°
  • (ii)
    138°
  • (iii)
    158°
  • (iv)
    128°
  • (v)
    143°
Question 65
65.
In the given figure, ∠GFE = 50° & ∠OHE = 41°, find ∠OIH
  • (i)
    24°
  • (ii)
    34°
  • (iii)
    29°
  • (iv)
    54°
  • (v)
    39°
    Assignment Key

  •  1) (v)
  •  2) (iii)
  •  3) (iii)
  •  4) (i)
  •  5) (iii)
  •  6) (ii)
  •  7) (v)
  •  8) (v)
  •  9) (v)
  •  10) (iv)
  •  11) (i)
  •  12) (ii)
  •  13) (iii)
  •  14) (iv)
  •  15) (ii)
  •  16) (i)
  •  17) (i)
  •  18) (iii)
  •  19) (i)
  •  20) (iv)
  •  21) (v)
  •  22) (iv)
  •  23) (iv)
  •  24) (v)
  •  25) (ii)
  •  26) (iv)
  •  27) (i)
  •  28) (iii)
  •  29) (i)
  •  30) (ii)
  •  31) (v)
  •  32) (iii)
  •  33) (iv)
  •  34) (iii)
  •  35) (v)
  •  36) (iv)
  •  37) (i)
  •  38) (iii)
  •  39) (i)
  •  40) (iv)
  •  41) (v)
  •  42) (iii)
  •  43) (iii)
  •  44) (v)
  •  45) (i)
  •  46) (i)
  •  47) (i)
  •  48) (v)
  •  49) (iii)
  •  50) (iv)
  •  51) (i)
  •  52) (iv)
  •  53) (i)
  •  54) (i)
  •  55) (ii)
  •  56) (v)
  •  57) (iii)
  •  58) (iii)
  •  59) (v)
  •  60) (i)
  •  61) (v)
  •  62) (iv)
  •  63) (ii)
  •  64) (iv)
  •  65) (i)