ICSE Board Practice

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ICSE Grade X - Tangent Properties of Circles
Question 1
1.
A line which intersects the circle at two distinct points is called a
  • chord
  • circumference
  • centre
  • secant
  • major segment
Question 2
2.
With the vertices of a triangle △FGH as centres, three circles are drawn touching each other externally. If the sides of the triangle are 9 cm , 16 cm and 11 cm , find the radii of the circles
  • 7 cm , 12 cm & 14 cm respectively
  • 2 cm , 7 cm & 14 cm respectively
  • 7 cm , 7 cm & 9 cm respectively
  • 2 cm , 7 cm & 9 cm respectively
  • 2 cm , 12 cm & 9 cm respectively
Question 3
3.
If two circles of radii 15 cm and 7 cm touch internally, the distance between their centres is
  • 10 cm
  • 8 cm
  • 9 cm
  • 7 cm
  • 6 cm
Question 4
4.
In the given figure, O is the centre of the circle and KL is the tangent at J. If ∠JHI = 53°, find ∠KJI
  • 68°
  • 53°
  • 83°
  • 58°
  • 63°
Question 5
5.
In the given figure, JKLM is a cyclic quadrilateral such that LJ bisects ∠MJK and NO is the tangent at L. If ∠LJK = 56°, find ∠NLK
  • 66°
  • 86°
  • 71°
  • 61°
  • 56°
Question 6
6.
If two circles of radii 10 cm and 7 cm touch externally, the distance between their centres is
  • 18 cm
  • 15 cm
  • 16 cm
  • 17 cm
  • 19 cm
Question 7
7.
If 'l' is the length of the tangent drawn to a circle with radius 'r' from point 'P' which is 'd' cm away from the centre, then
  • r
    =
    √
    (
    l
    2
     
    +
    d
    2
     
    		)
  • d
    =
    √
    (
    l
    2
     
    −
    r
    2
     
    		)
  • l
    =
    √
    (
    d
    2
     
    −
    r
    2
     
    		)
  • l
    =
    √
    (
    d
    2
     
    +
    r
    2
     
    		)
  • d
    =
    √
    (
    l
    2
     
    +
    r
    2
     
    		)
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
  • tangent
  • secant
  • quadrant
  • segment
  • semi-circle
Question 9
9.
O is the centre of the circumcircle of △EFG. Tangents at E and G intersect at H. If ∠EHG = 70.31°, find ∠GFE
  • 59.84°
  • 54.84°
  • 64.84°
  • 69.84°
  • 84.84°
Question 10
10.
Which of the following statements are true?
a)
Only one tangent can be drawn through a point on a circle.
b)
Two tangents to a circle always intersect.
c)
Only two tangents can be drawn from a point outside the circle.
d)
Atmost one tangent can be drawn through a point inside the circle.
e)
The sides of a triangle can be tangents to a circle.
  • {b,a,c}
  • {d,c}
  • {b,a}
  • {a,c,e}
  • {b,d,e}