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, AT & BT are tangents to the circle with centre O. Given ∠AOB = 123°, find ∠ATB
  • 57°
  • 62°
  • 87°
  • 67°
  • 72°
Question 2
2.
If two circles of radii 10 cm and 4 cm touch internally, the distance between their centres is
  • 8 cm
  • 6 cm
  • 5 cm
  • 7 cm
  • 4 cm
Question 3
3.
O is the centre of the circumcircle of △ABC. Tangents at A and C intersect at D. If ∠ADC = 70.17°, find ∠CBA
  • 69.91°
  • 64.91°
  • 54.91°
  • 84.91°
  • 59.91°
Question 4
4.
Which of the following statements are true?
a)
A secant has two end points.
b)
A radius is a limiting case of a diameter.
c)
A tangent is the limiting case of a secant.
d)
A diameter is a limiting case of a chord.
e)
A secant and a chord are same.
  • {a,c}
  • {b,d,c}
  • {e,a,c}
  • {b,d}
  • {c,d}
Question 5
5.
    • 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
  • None of these
  • √
    d
    2
    −
    (
    r

    1
    		  +  
    r

    2
    )
    2
  • √
    d
    2
    +
    (
    r

    1
    		  −  
    r

    2
    )
    2
Question 6
6.
    • If two circles
    • touch externally
    • ,
    • the number of their common tangents is
  • 1
  • 2
  • 6
  • 4
  • 3
Question 7
7.
Two circles with radii R and r touch internally. If the distance between their centres is d, then
  • d > R - r
  • d < R - r
  • d = R - r
  • d < R + r
  • d = R + r
Question 8
8.
O is the centre of the circumcircle of △DEF. Tangents at D and E intersect at G. If ∠DGE = 54.76° and ∠DOF = 110°, find ∠FDE
  • 72.38°
  • 67.38°
  • 77.38°
  • 92.38°
  • 62.38°
Question 9
9.
In the given figure, O is the centre of the circle and MN is the tangent at J. If ∠KJL = 55° and ∠MJK = 97°, find ∠JLK
  • 47°
  • 72°
  • 52°
  • 42°
  • 57°
Question 10
10.
    • The distance between the centres of two circles is
    • d
    • .
    • If the radii are
    • r

      1
    • and
    • r

      2
    • ,
    • the length of their direct 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