EduSahara™ Worksheet

Question 1

1.

In the given figure, O is the centre of the circle and JK is the tangent at F. If ∠FIH = 49°, find ∠FGH

(i)

131°
(ii)

141°
(iii)

146°
(iv)

161°
(v)

136°

Question 2

2.

In the given figure, two circles intersect at points F & G. A tangent is drawn at point H. From the same point, two lines are drawn passing through points F & G. They meet the other end of the second circle at E & D. Given ∠H = 56°, find ∠DGF

(i)

134°
(ii)

124°
(iii)

129°
(iv)

154°
(v)

139°

Question 3

3.

Two circles with equal radii are

(i)

concentric
(ii)

not similar
(iii)

congruent
(iv)

only similar but not congruent

Question 4

4.

A line which intersects the circle at two distinct points is called a

(i)

major segment
(ii)

secant
(iii)

chord
(iv)

semi-circle
(v)

quadrant

Question 5

5.

In the given figure, DG is the common tangent to the two circles. DE & DF are also tangents. Given DE = 22 cm, find DF

(i)

22 cm
(ii)

23 cm
(iii)

20 cm
(iv)

24 cm
(v)

21 cm

Question 6

6.

If two circles of radii 8 cm and 7 cm touch externally, the distance between their centres is

(i)

17 cm
(ii)

13 cm
(iii)

16 cm
(iv)

15 cm
(v)

14 cm

Question 7

7.

In the given figure, O is the centre of the circle and IJ is the tangent at H. If ∠HGF = 39°, find ∠JHF

(i)

54°
(ii)

44°
(iii)

49°
(iv)

39°
(v)

69°

Question 8

8.

A line which touches a circle at only one point is called a

(i)

segment
(ii)

tangent
(iii)

circumference
(iv)

chord
(v)

diameter

Question 9

9.

The distance between the centres of two circles is
d
.

If the radii are
r

1
and
r

2
,
the length of their direct common tangent is

(i)

√

d

2

+

(

r

1

−

r

2

)

2
(ii)

√

d

2

−

(

r

1

−

r

2

)

2
(iii)

√

d

2

+

(

r

1

+

r

2

)

2
(iv)

None of these
(v)

√

d

2

−

(

r

1

+

r

2

)

2

Question 10

10.

With the vertices of a triangle △FGH as centres, three circles are drawn touching each other externally. If the sides of the triangle are 8 cm , 14 cm and 10 cm , find the radii of the circles

(i)

7 cm , 11 cm & 13 cm respectively
(ii)

2 cm , 11 cm & 8 cm respectively
(iii)

2 cm , 6 cm & 13 cm respectively
(iv)

7 cm , 6 cm & 8 cm respectively
(v)

2 cm , 6 cm & 8 cm respectively

Question 11

11.

JK is a line segment and M is its mid-point. Three semi-circles are drawn with JM , MK and JK as diameters. L , N and M respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given JL = 5 cm

(i)

4.33 cm
(ii)

5.33 cm
(iii)

3.33 cm
(iv)

2.33 cm
(v)

1.33 cm

Question 12

12.

In the given figure, O is the centre of the circle and HI is the tangent at G. If ∠FDG = 43° and ∠DFE = 63°, find ∠HGF

(i)

43°
(ii)

73°
(iii)

53°
(iv)

58°
(v)

48°

Question 13

13.

Which of the following statements are true?

a)	If two circles touch internally, the distance between their centres is the difference of their radii.
b)	If two circles touch externally, the distance between their centres is the sum of their radii.
c)	If two circles touch externally, the square of the distance between their centres is the sum of the squares of their radii.
d)	If two circles touch externally, their centres and the point of contact form an isosceles triangle.
e)	If two circles touch internally, their centres and the point of contact form a scalene triangle.
f)	If two circles touch internally, the square of the distance between their centres is the difference of the squares of their radii.

(i)

{c,a}
(ii)

{e,f,a}
(iii)

{d,b}
(iv)

{c,b,a}
(v)

{a,b}

Question 14

14.

In the given figure, O is the centre of the circle and FH is the tangent at G. If ∠GHI = 47°,∠HGI = 33°, find ∠JGI

(i)

77°
(ii)

67°
(iii)

97°
(iv)

72°
(v)

82°

Question 15

15.

Which of the following statements are true?

a)	Atmost three common tangents can be drawn touching two circles which touch each other.
b)	Atmost two common tangents can be drawn touching any two circles.
c)	A maximum of four common tangents can be drawn touching any two circles.
d)	Atmost one common tangent can be drawn for any two concentric circles.

(i)

{b,a}
(ii)

{b,d,a}
(iii)

{a,c}
(iv)

{b,c,a}
(v)

{d,c}

Question 16

16.

In the given figure, O is the centre of the circle and DE is the tangent at A. If ∠BAC = 41° and ∠DAB = 47°, find ∠CAE

(i)

102°
(ii)

122°
(iii)

97°
(iv)

92°
(v)

107°

Question 17

17.

If the two radii OP and OQ of a circle are at right angles to each other, then the sector OPQ is called a

(i)

segment
(ii)

quadrant
(iii)

major segment
(iv)

diameter
(v)

tangent

Question 18

18.

In the given figure, CR & DR are tangents to the circle with centre O. Given ∠C = 22°, find ∠R

(i)

59°
(ii)

49°
(iii)

54°
(iv)

74°
(v)

44°

Question 19

19.

In the given figure, EF and GH are parallel tangents to the circle with centre O. EH is another tangent meeting EF and GH at E and H. Find ∠EOH

(i)

90°
(ii)

95°
(iii)

105°
(iv)

120°
(v)

100°

Question 20

20.

In the given figure, DS & ES are tangents to the circle with centre O. Given ∠DOE = 122°, find ∠DSE

(i)

63°
(ii)

58°
(iii)

88°
(iv)

73°
(v)

68°

Question 21

21.

In the given figure, two circles intersect at points K & L. A tangent is drawn at point M. From the same point, two lines are drawn passing through points K & L. They meet the other end of the second circle at J & I. Given ∠M = 55°, find ∠IJK

(i)

85°
(ii)

70°
(iii)

55°
(iv)

65°
(v)

60°

Question 22

22.

If two circles
intersect
,
the number of their common tangents is

(i)

3
(ii)

(-1)
(iii)

1
(iv)

2
(v)

4

Question 23

23.

Which of the following statements are true?

a)	An infinite number of chords may be drawn for a circle.
b)	Every circle has a unique diameter.
c)	An infinite number of diameters may be drawn for a circle.
d)	One and only one tangent can be drawn to a circle from a point outside it.
e)	Two semi-circles of a circle together make the whole circle.

(i)

{d,c}
(ii)

{b,d,e}
(iii)

{a,c,e}
(iv)

{b,a}
(v)

{b,a,c}

Question 24

24.

Which of the following statements are true?

a)	A radius is a limiting case of a diameter.
b)	A secant and a chord are same.
c)	A diameter is a limiting case of a chord.
d)	A tangent is the limiting case of a secant.
e)	A secant has two end points.

(i)

{e,a,c}
(ii)

{b,d}
(iii)

{b,d,c}
(iv)

{c,d}
(v)

{a,c}

Question 25

25.

In the given figure, O is the centre of the circle and HI is the tangent at G. If ∠GEF = 63°, find ∠HGF

(i)

73°
(ii)

68°
(iii)

78°
(iv)

93°
(v)

63°

Assignment Key