ICSE Board Practice

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ICSE Grade X - Tangent Properties of Circles
Question 1
1.
In the given figure, O is the centre of the circle and EF is the tangent at D. If ∠CAD = 52° and ∠ACB = 50°, find ∠EDC
  • 52°
  • 62°
  • 57°
  • 67°
  • 82°
Question 2
2.
In the given figure, GE and GF are tangent segments to the circle with centre O. Given ∠FGH = 20°, find ∠EFH
  • 35°
  • 65°
  • 40°
  • 50°
  • 45°
Question 3
3.
The angle between a tangent to a circle and the radius drawn at the point of contact is
  • 90°
  • 100°
  • 95°
  • 120°
  • 105°
Question 4
4.
Two circles are of radii 1 cm and 3 cm. If the distance between their centres is 9 cm, what is the length of their direct common tangent?
  • 9.77 cm
  • 8.77 cm
  • 10.77 cm
  • 6.77 cm
  • 7.77 cm
Question 5
5.
In the given figure, O is the centre of the circle and LM is the tangent at I. If ∠OJI = 38°, find ∠MIJ
  • 82°
  • 67°
  • 52°
  • 62°
  • 57°
Question 6
6.
With the vertices of a triangle △IJK as centres, three circles are drawn touching each other externally. If the sides of the triangle are 11 cm , 14 cm and 13 cm , find the radii of the circles
  • 10 cm , 11 cm & 13 cm respectively
  • 10 cm , 6 cm & 8 cm respectively
  • 5 cm , 6 cm & 8 cm respectively
  • 5 cm , 6 cm & 13 cm respectively
  • 5 cm , 11 cm & 8 cm respectively
Question 7
7.
Which of the following statements are true?
a)
If two tangents are parallel, the distance between them is equal to the diameter of the circle.
b)
Two different tangents can meet at a point on the circle.
c)
If two tangents are perpendicular, they form a right angled triangle with their points of contact with the circle and their point of intersection.
d)
A line parallel to a tangent is a secant.
e)
If two tangents to a circle intersect, their points of contact with the circle together with their point of intersection form an isosceles triangle.
  • {b,a}
  • {a,c,e}
  • {b,a,c}
  • {d,c}
  • {b,d,e}
Question 8
8.
    • If two circles
    • touch internally
    • ,
    • the number of their common tangents is
  • 4
  • 0
  • (-1)
  • 2
  • 1
Question 9
9.
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
  • quadrant
  • diameter
  • secant
  • circumference
Question 10
10.
    • If two circles
    • intersect
    • ,
    • the number of their common tangents is
  • 2
  • 5
  • 3
  • 0
  • 1