ICSE Board Practice

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ICSE Grade X - Tangent Properties of Circles
Question 1
1.
A line which touches a circle at only one point is called a
  • diameter
  • quadrant
  • semi-circle
  • tangent
  • major segment
Question 2
2.
Which of the following statements are true?
a)
One and only one tangent can be drawn to pass through a point on a circle.
b)
A secant of a circle is a segment having its end points on the circle.
c)
One and only one tangent can be drawn to a circle from a point outside it.
d)
Diameter of a circle is a part of the semi-circle of the circle.
e)
Every circle has a unique diameter.
  • {c,d,a}
  • {e,b,a}
  • {b,a}
  • {c,d}
  • {a,d}
Question 3
3.
In the given figure, two circles intersect at points C & D. A tangent is drawn at point E. From the same point, two lines are drawn passing through points C & D. They meet the other end of the second circle at B & A. Given ∠E = 84°, find ∠BAD
  • 84°
  • 94°
  • 89°
  • 99°
  • 114°
Question 4
4.
In the given figure, EH is the common tangent to the two circles. EF & EG are also tangents. Given EF = 16 cm, find EG
  • 15 cm
  • 16 cm
  • 17 cm
  • 14 cm
  • 18 cm
Question 5
5.
Two circles with equal radii are
  • only similar but not congruent
  • congruent
  • not similar
  • concentric
Question 6
6.
In the given figure, O is the centre of the circle and IJ is the tangent at H. If ∠GEH = 53° and ∠EGF = 41°, find ∠GEF
  • 54°
  • 79°
  • 64°
  • 59°
  • 49°
Question 7
7.
In the given figure, O is the centre of the circle and GH is the tangent at D. If ∠OED = 30°, find ∠HDE
  • 70°
  • 65°
  • 90°
  • 75°
  • 60°
Question 8
8.
    • 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 9
9.
Which of the following statements are true?
a)
A tangent is the limiting case of a secant.
b)
A radius is a limiting case of a diameter.
c)
A secant and a chord are same.
d)
A secant has two end points.
e)
A diameter is a limiting case of a chord.
  • {d,b,a}
  • {c,e,a}
  • {b,a}
  • {c,e}
  • {a,e}
Question 10
10.
    • If two circles
    • intersect
    • ,
    • the number of their common tangents is
  • 1
  • (-1)
  • 3
  • 5
  • 2