EduSahara™ Worksheet

Question 1

1.

With the vertices of a triangle △IJK as centres, three circles are drawn touching each other externally. If the sides of the triangle are 10 cm , 15 cm and 15 cm , find the radii of the circles

(i)

10 cm , 5 cm & 10 cm respectively
(ii)

5 cm , 10 cm & 10 cm respectively
(iii)

10 cm , 10 cm & 15 cm respectively
(iv)

5 cm , 5 cm & 10 cm respectively
(v)

5 cm , 5 cm & 15 cm respectively

Question 2

2.

O is the centre of the circumcircle of △ABC. Tangents at A and B intersect at D. If ∠ADB = 70.36° and ∠AOC = 140°, find ∠CAB

(i)

55.18°
(ii)

60.18°
(iii)

70.18°
(iv)

65.18°
(v)

85.18°

Question 3

3.

In the given figure, EC and ED are tangent segments to the circle with centre O. Given ∠DEF = 29°, find ∠CDF

(i)

45.5°
(ii)

30.5°
(iii)

60.5°
(iv)

40.5°
(v)

35.5°

Question 4

4.

In the given figure, IJKL is a cyclic quadrilateral such that KI bisects ∠LIJ and MN is the tangent at K. If ∠KIJ = 57°, find ∠MKJ

(i)

67°
(ii)

62°
(iii)

87°
(iv)

57°
(v)

72°

Question 5

5.

If two circles
touch internally
,
the number of their common tangents is

(i)

1
(ii)

2
(iii)

(-2)
(iv)

0
(v)

4

Question 6

6.

Which of the following statements are true?

a)	Two tangents to a circle always intersect.
b)	Only two tangents can be drawn from a point outside the circle.
c)	Atmost one tangent can be drawn through a point inside the circle.
d)	Only one tangent can be drawn through a point on a circle.
e)	The sides of a triangle can be tangents to a circle.

(i)

{b,d,e}
(ii)

{a,c,e}
(iii)

{a,b}
(iv)

{c,d}
(v)

{a,b,d}

Question 7

7.

In the given figure, two circles intersect at points D & E. A tangent is drawn at point F. From the same point, two lines are drawn passing through points D & E. They meet the other end of the second circle at C & B. Given ∠F = 65°, find ∠BED

(i)

130°
(ii)

115°
(iii)

120°
(iv)

125°
(v)

145°

Question 8

8.

In the given figure, DB and DC are tangent segments to the circle with centre O. Given ∠CDE = 37°, find ∠BCO

(i)

37°
(ii)

52°
(iii)

42°
(iv)

67°
(v)

47°

Question 9

9.

In the given figure, O is the centre of the circle and IJ is the tangent at E. If ∠EHG = 49°, find ∠JEG

(i)

49°
(ii)

59°
(iii)

79°
(iv)

64°
(v)

54°

Question 10

10.

Which of the following statements are true?

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

(i)

{a,b}
(ii)

{a,b,c}
(iii)

{a,e,d}
(iv)

{b,c,d}
(v)

{e,c}

Question 11

11.

In the given figure, O is the centre of the circle and FH is the tangent at G. If ∠EDG = 29°, find ∠EFG + ∠EGF

(i)

91°
(ii)

76°
(iii)

66°
(iv)

71°
(v)

61°

Question 12

12.

In the given figure, O is the centre of the circle and the tangents CF and EF meet at point F. If ∠DEC = 47°, find ∠COE

(i)

124°
(ii)

99°
(iii)

109°
(iv)

104°
(v)

94°

Question 13

13.

In the given figure, O is the centre of the circle and HJ is the tangent at I . If ∠GFI = 29°, find ∠GHI

(i)

37°
(ii)

47°
(iii)

42°
(iv)

32°
(v)

62°

Question 14

14.

In the given figure, O is the centre of the circle and EF is the tangent at D. If ∠DCB = 47°, find ∠FDB

(i)

57°
(ii)

52°
(iii)

62°
(iv)

77°
(v)

47°

Question 15

15.

Which of the following statements are true?

a)	If two circles touch each other internally, there is only one common tangent.
b)	If two circles touch each other externally, there is only one common tangent.
c)	If two circles intersect, then two common tangents can be drawn.
d)	There exists four common tangents for any two non-intersecting circles.

(i)

{b,d}
(ii)

{b,a}
(iii)

{b,c}
(iv)

{a,c,d}
(v)

{b,a,c}

Question 16

16.

Two circles are of radii 6 cm and 3 cm. If the distance between their centres is 10 cm, what is the length of their direct common tangent?

(i)

10.54 cm
(ii)

9.54 cm
(iii)

8.54 cm
(iv)

7.54 cm
(v)

11.54 cm

Question 17

17.

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)

None of these
(ii)

√

d

2

−

(

r

1

−

r

2

)

2
(iii)

√

d

2

+

(

r

1

−

r

2

)

2
(iv)

√

d

2

−

(

r

1

+

r

2

)

2
(v)

√

d

2

+

(

r

1

+

r

2

)

2

Question 18

18.

CD is a line segment and F is its mid-point. Three semi-circles are drawn with CF , FD and CD as diameters. E , G and F respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given CE = 6 cm

(i)

4.00 cm
(ii)

2.00 cm
(iii)

3.00 cm
(iv)

5.00 cm
(v)

6.00 cm

Question 19

19.

Two circles with equal radii are

(i)

congruent
(ii)

only similar but not congruent
(iii)

not similar
(iv)

concentric

Question 20

20.

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

(i)

l

=

√

(

d

2

+

r

2

)
(ii)

r

=

√

(

l

2

+

d

2

)
(iii)

l

=

√

(

d

2

−

r

2

)
(iv)

d

=

√

(

l

2

−

r

2

)
(v)

d

=

√

(

l

2

+

r

2

)

Question 21

21.

If two circles of radii 14 cm and 5 cm touch externally, the distance between their centres is

(i)

18 cm
(ii)

17 cm
(iii)

19 cm
(iv)

21 cm
(v)

20 cm

Question 22

22.

In the given figure, CF is the common tangent to the two circles. CD & CE are also tangents. Given CD = 11 cm, find CE

(i)

9 cm
(ii)

11 cm
(iii)

13 cm
(iv)

12 cm
(v)

10 cm

Question 23

23.

In the given figure, O is the centre of the circle and KL is the tangent at J. If ∠IGJ = 61° and ∠GIH = 49°, find ∠KJI

(i)

91°
(ii)

71°
(iii)

61°
(iv)

66°
(v)

76°

Question 24

24.

Two circles with radii R and r touch internally. If the distance between their centres is d, then

(i)

d < R + r
(ii)

d < R - r
(iii)

d = R + r
(iv)

d > R - r
(v)

d = R - r

Question 25

25.

Two circles are of radii 6 cm and 5 cm. If the distance between their centres is 17 cm, what is the length of their transverse common tangent?

(i)

14.96 cm
(ii)

11.96 cm
(iii)

12.96 cm
(iv)

10.96 cm
(v)

13.96 cm

Assignment Key