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)