CBSE Board Practice

Class VI Class VII Class VIII Class IX Class X
CBSE Grade X - Circles
Question 1
1.
O is the centre of the circle. FG and HG are tangents to the circle. If ∠HIF = 30.5°, find ∠FGH
  • 134°
  • 119°
  • 129°
  • 149°
  • 124°
Question 2
2.
In the given figure, O is the centre of the circle and FH is the tangent at G . If ∠EDG = 30°, find ∠EFG
  • 30°
  • 60°
  • 40°
  • 35°
  • 45°
Question 3
3.
    • If two circles
    • touch externally
    • ,
    • the number of their common tangents is
  • 0
  • 4
  • 6
  • 3
  • 2
Question 4
4.
With the vertices of a triangle △GHI as centres, three circles are drawn touching each other externally. If the sides of the triangle are 8 cm , 14 cm and 12 cm , find the radii of the circles
  • 3 cm , 10 cm & 9 cm respectively
  • 3 cm , 5 cm & 9 cm respectively
  • 8 cm , 10 cm & 14 cm respectively
  • 3 cm , 5 cm & 14 cm respectively
  • 8 cm , 5 cm & 9 cm respectively
Question 5
5.
Which of the following statements are true?
a)
If two circles touch internally, their centres and the point of contact form a scalene triangle.
b)
If two circles touch externally, their centres and the point of contact form an isosceles triangle.
c)
If two circles touch internally, the square of the distance between their centres is the difference of the squares of their radii.
d)
If two circles touch externally, the square of the distance between their centres is the sum of the squares of their radii.
e)
If two circles touch externally, the distance between their centres is the sum of their radii.
f)
If two circles touch internally, the distance between their centres is the difference of their radii.
  • {b,f}
  • {e,f}
  • {a,e}
  • {c,d,e}
  • {a,f,e}
Question 6
6.
The point of intersection of the angular bisectors of a triangle is
  • circumcentre
  • excentre
  • centroid
  • orthocentre
  • incentre
Question 7
7.
Which of the following statements are true?
a)
There exists four common tangents for any two non-intersecting circles.
b)
If two circles touch each other internally, there is only one common tangent.
c)
If two circles intersect, then two common tangents can be drawn.
d)
If two circles touch each other externally, there is only one common tangent.
  • {a,b,c}
  • {d,b}
  • {d,a}
  • {d,a,b}
  • {d,c}
Question 8
8.
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
  • l
    =
    √
    (
    d
    2
     
    −
    r
    2
     
    		)
  • r
    =
    √
    (
    l
    2
     
    +
    d
    2
     
    		)
  • l
    =
    √
    (
    d
    2
     
    +
    r
    2
     
    		)
  • d
    =
    √
    (
    l
    2
     
    +
    r
    2
     
    		)
  • d
    =
    √
    (
    l
    2
     
    −
    r
    2
     
    		)
Question 9
9.
In the given figure, O is the centre of the circle and IJ is the tangent at H. If ∠HFG = 55°, find ∠IHG
  • 60°
  • 65°
  • 70°
  • 85°
  • 55°
Question 10
10.
If two circles of radii 8 cm and 7 cm touch externally, the distance between their centres is
  • 14 cm
  • 17 cm
  • 15 cm
  • 13 cm
  • 16 cm