ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Angle Properties of a Circle
Question 1
1.
In the given figure, which of the following are true?
a)
    • ∠J
    • +
    • ∠OLK = 90°
b)
    • ∠J
    • +
    • ∠OKL
    • +
    • ∠OLK
    • =
    • 2
    • ∠J
c)
    • ∠J
    • +
    • ∠KOL = 180°
d)
    • ∠J
    • +
    • ∠OKL = 90°
e)
    • ∠J
    • +
    • ∠OKL = 120°
  • {a,d}
  • {c,d,a}
  • {c,d}
  • {e,b,a}
  • {b,a}
Question 2
2.
In the given figure, chords EG & FH meet at I. Given x = 116° and y = 47°, find ∠FEG
  • 84°
  • 99°
  • 69°
  • 74°
  • 79°
Question 3
3.
Which of the following statements are true?
a)
All parallelograms are cyclic.
b)
An isosceles trapezium is cyclic.
c)
A quadrilateral in which the diagonals are equal and bisect each other is cyclic.
d)
The exterior angle of a quadrilateral and its interior opposite angle are supplementary.
e)
Either pair of opposite angles of a cyclic quadrilateral are supplementary.
  • {a,b}
  • {a,d,e}
  • {b,c,e}
  • {d,c}
  • {a,b,c}
Question 4
4.
In the given figure, ABCDEF is a regular hexagon. Find ∠ACB
  • 45°
  • 30°
  • 60°
  • 35°
  • 40°
Question 5
5.
Two circles touch internally. F is the centre of the bigger circle and lies on the smaller circle. If ∠CDE = 63°, find ∠C
  • 42°
  • 27°
  • 57°
  • 37°
  • 32°
Question 6
6.
In the given figure, △KGH is a scalene triangle. IG & JG trisect ∠KGH. Similarly HI & HJ trisect ∠GHK. Given ∠HKG = 54°, find ∠HJG
  • 101°
  • 126°
  • 111°
  • 96°
  • 106°
Question 7
7.
In the given figure, O is the centre of the circle. If ∠FGO = 9° and ∠OIF = 41°, find ∠GOI
  • 110°
  • 100°
  • 105°
  • 130°
  • 115°
Question 8
8.
In the given figure, ∠GIJ = 12° and ∠GKJ = 23°, find ∠HJG
  • 88°
  • 83°
  • 108°
  • 78°
  • 93°
Question 9
9.
Which of the following statements are true?
a)
A cyclic trapezium is a rectangle.
b)
A cyclic parallelogram is a rhombus.
c)
A cyclic rhombus is a square.
d)
A cyclic parallelogram is a rectangle.
e)
A cyclic kite is a square.
  • {a,c}
  • {e,a,c}
  • {c,d}
  • {b,d}
  • {b,d,c}
Question 10
10.
In the given figure, △IFG is a scalene triangle. HF bisects ∠IFG. Similarly GH bisects ∠FGI. Given ∠GIF = 126°, find ∠GHF
  • 158°
  • 183°
  • 168°
  • 153°
  • 163°