ICSE Board Practice

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ICSE Grade X - Tangent Properties of Circles
Question 1
1.
    • If two circles
    • touch internally
    • ,
    • the number of their common tangents is
  • (-2)
  • 0
  • 1
  • 4
  • 2
Question 2
2.
    • 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
  • None of these
  • √
    d
    2
    −
    (
    r

    1
    		  −  
    r

    2
    )
    2
Question 3
3.
O is the centre of the circumcircle of △FGH. Tangents at F and G intersect at I. If ∠FIG = 69.75° and ∠FOH = 140°, find ∠HFG
  • 69.88°
  • 59.88°
  • 54.88°
  • 84.88°
  • 64.88°
Question 4
4.
In the given figure, two circles intersect at points G & H. A tangent is drawn at point I. From the same point, two lines are drawn passing through points G & H. They meet the other end of the second circle at F & E. Given ∠I = 59°, find ∠EFG
  • 74°
  • 89°
  • 64°
  • 59°
  • 69°
Question 5
5.
In the given figure, O is the centre of the circle and DE is the tangent at A. If ∠BAC = 41° and ∠DAB = 41°, find ∠CAE
  • 113°
  • 98°
  • 128°
  • 103°
  • 108°
Question 6
6.
In the given figure, IG and IH are tangent segments to the circle with centre O. Given ∠HIJ = 34°, find ∠GHO
  • 49°
  • 64°
  • 39°
  • 34°
  • 44°
Question 7
7.
In the given figure, IJ and KL are parallel tangents to the circle with centre O. IL is another tangent meeting IJ and KL at I and L. Find ∠IOL
  • 100°
  • 95°
  • 120°
  • 105°
  • 90°
Question 8
8.
In the given figure, O is the centre of the circle and the tangents EH and GH meet at point H. If ∠FGE = 50°, find ∠EOG
  • 110°
  • 115°
  • 105°
  • 130°
  • 100°
Question 9
9.
In the given figure, O is the centre of the circle and IJ is the tangent at E. If ∠EHG = 57°, find ∠EFG
  • 133°
  • 153°
  • 128°
  • 138°
  • 123°
Question 10
10.
Which of the following statements are true?
a)
Atmost one common tangent can be drawn for any two concentric circles.
b)
Atmost two common tangents can be drawn touching any two circles.
c)
Atmost three common tangents can be drawn touching two circles which touch each other.
d)
A maximum of four common tangents can be drawn touching any two circles.
  • {a,b,c}
  • {a,d,c}
  • {a,c}
  • {b,d}
  • {c,d}