ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Tangent Properties of Circles
Question 1
1.
In the given figure, O is the centre of the circle and GH is the tangent at D. If ∠OED = 39°, find ∠HDE
  • 81°
  • 56°
  • 61°
  • 51°
  • 66°
Question 2
2.
In the given figure, O is the centre of the circle and the tangents BE and DE meet at point E. If ∠CDB = 57°, find ∠DEB
  • 81°
  • 96°
  • 71°
  • 76°
  • 66°
Question 3
3.
    • If two circles
    • touch internally
    • ,
    • the number of their common tangents is
  • (-1)
  • 0
  • 4
  • 1
  • 2
Question 4
4.
In the given figure, two circles intersect at points D & E. A tangent is drawn at point F. From the same point, two lines are drawn passing through points D & E. They meet the other end of the second circle at C & B. Given ∠F = 81°, find ∠CBE
  • 111°
  • 81°
  • 96°
  • 86°
  • 91°
Question 5
5.
In the given figure, two circles intersect at points I & J. A tangent is drawn at point K. From the same point, two lines are drawn passing through points I & J. They meet the other end of the second circle at H & G. Given ∠K = 85°, find ∠HIJ
  • 95°
  • 125°
  • 105°
  • 110°
  • 100°
Question 6
6.
    • If two circles
    • intersect
    • ,
    • the number of their common tangents is
  • 3
  • 5
  • 1
  • 0
  • 2
Question 7
7.
Which of the following statements are true?
a)
Only two tangents can be drawn from a point outside the circle.
b)
Two tangents to a circle always intersect.
c)
The sides of a triangle can be tangents to a circle.
d)
Atmost one tangent can be drawn through a point inside the circle.
e)
Only one tangent can be drawn through a point on a circle.
  • {b,a,c}
  • {b,d,e}
  • {d,c}
  • {b,a}
  • {a,c,e}
Question 8
8.
If the two radii OP and OQ of a circle are at right angles to each other, then the sector OPQ is called a
  • quadrant
  • major segment
  • centre
  • circumference
  • tangent
Question 9
9.
    • The distance between the centres of two circles is
    • d
    • .
    • If the radii are
    • r

      1
    • and
    • r

      2
    • ,
    • the length of their transverse common tangent is
  • √
    d
    2
    −
    (
    r

    1
    		  −  
    r

    2
    )
    2
  • √
    d
    2
    −
    (
    r

    1
    		  +  
    r

    2
    )
    2
  • √
    d
    2
    +
    (
    r

    1
    		  +  
    r

    2
    )
    2
  • √
    d
    2
    +
    (
    r

    1
    		  −  
    r

    2
    )
    2
  • None of these
Question 10
10.
O is the centre of the circumcircle of △DEF. Tangents at D and E intersect at G. If ∠DGE = 54.83° and ∠DOF = 110°, find ∠FDE
  • 62.41°
  • 92.41°
  • 67.41°
  • 72.41°
  • 77.41°