EduSahara™ Worksheet

Question 1

1.

Which of the following statements are true?

a)	Every circle has a unique diameter.
b)	Each radius of a circle is also a chord of the circle.
c)	A circle consists of an infinite number of points.
d)	Every circle has a unique centre.
e)	A line can meet a circle atmost at two points.

(i)

{a,b,e}
(ii)

{a,c,d}
(iii)

{c,d,e}
(iv)

{b,d}
(v)

{a,c}

Question 2

2.

Which of the following statements are true?

a)	Every circle has a unique diameter.
b)	A secant of a circle is a segment having its end points on the circle.
c)	One and only one tangent can be drawn to a circle from a point outside it.
d)	Diameter of a circle is a part of the semi-circle of the circle.
e)	One and only one tangent can be drawn to pass through a point on a circle.

(i)

{d,e}
(ii)

{a,d}
(iii)

{c,a,d}
(iv)

{b,e,d}
(v)

{b,e}

Question 3

3.

Find the missing angle in the following figure?

(i)

57°
(ii)

47°
(iii)

62°
(iv)

52°
(v)

77°

Question 4

4.

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)

l

=

√

(

d

2

+

r

2

)
(iii)

r

=

√

(

l

2

+

d

2

)
(iv)

d

=

√

(

l

2

−

r

2

)
(v)

d

=

√

(

l

2

+

r

2

)

Question 5

5.

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 6

6.

The angle between a tangent to a circle and the radius drawn at the point of contact is

(i)

95°
(ii)

90°
(iii)

105°
(iv)

120°
(v)

100°

Question 7

7.

If two circles of radii 9 cm and 7 cm touch internally, the distance between their centres is

(i)

3 cm
(ii)

4 cm
(iii)

1 cm
(iv)

2 cm
(v)

0 cm

Question 8

8.

If two circles of radii 11 cm and 3 cm touch externally, the distance between their centres is

(i)

16 cm
(ii)

15 cm
(iii)

12 cm
(iv)

13 cm
(v)

14 cm

Question 9

9.

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

(i)

2
(ii)

3
(iii)

0
(iv)

1
(v)

(-2)

Question 10

10.

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

(i)

0
(ii)

4
(iii)

2
(iv)

3
(v)

1

Question 11

11.

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

(i)

1
(ii)

5
(iii)

2
(iv)

4
(v)

3

Question 12

12.

O is the centre of the circumcircle of △ABC. Tangents at A and B intersect at D. If ∠ADB = 54.64° and ∠AOC = 110°, find ∠CAB

(i)

92.32°
(ii)

77.32°
(iii)

62.32°
(iv)

67.32°
(v)

72.32°

Question 13

13.

O is the centre of the circumcircle of △EFG. Tangents at E and G intersect at H. If ∠EHG = 70.16°, find ∠GFE

(i)

84.92°
(ii)

69.92°
(iii)

54.92°
(iv)

64.92°
(v)

59.92°

Question 14

14.

In the given figure, O is the centre of the circle and KL is the tangent at H. If ∠IHJ = 51° and ∠KHI = 96°, find ∠HJI

(i)

50°
(ii)

75°
(iii)

60°
(iv)

55°
(v)

45°

Question 15

15.

In the given figure, O is the centre of the circle and MN is the tangent at J. If ∠KJL = 39° and ∠MJK = 44°, find ∠LJN

(i)

127°
(ii)

112°
(iii)

97°
(iv)

107°
(v)

102°

Question 16

16.

In the given figure, O is the centre of the circle and FH is the tangent at G . If ∠EDG = 26°, find ∠EFG

(i)

38°
(ii)

68°
(iii)

48°
(iv)

53°
(v)

43°

Question 17

17.

In the given figure, O is the centre of the circle and HJ is the tangent at I. If ∠GFI = 25°, find ∠GHI + ∠GIH

(i)

70°
(ii)

65°
(iii)

95°
(iv)

80°
(v)

75°

Question 18

18.

In the given figure, O is the centre of the circle and DE is the tangent at C. If ∠CBA = 42°, find ∠ECA

(i)

47°
(ii)

52°
(iii)

57°
(iv)

42°
(v)

72°

Question 19

19.

In the given figure, O is the centre of the circle and HI is the tangent at G. If ∠GEF = 44°, find ∠HGF

(i)

44°
(ii)

74°
(iii)

49°
(iv)

54°
(v)

59°

Question 20

20.

In the given figure, O is the centre of the circle and KL is the tangent at J. If ∠IGJ = 34° and ∠GIH = 56°, find ∠LJG

(i)

66°
(ii)

56°
(iii)

61°
(iv)

86°
(v)

71°

Question 21

21.

In the given figure, O is the centre of the circle and EF is the tangent at D. If ∠CAD = 51° and ∠ACB = 40°, find ∠CAB

(i)

65°
(ii)

80°
(iii)

60°
(iv)

55°
(v)

50°

Question 22

22.

In the given figure, O is the centre of the circle and EF is the tangent at D. If ∠CAD = 30° and ∠ACB = 49°, find ∠EDC

(i)

30°
(ii)

45°
(iii)

35°
(iv)

60°
(v)

40°

Question 23

23.

In the given figure, O is the centre of the circle and DE is the tangent at A. If ∠OBA = 33.5°, find ∠EAB

(i)

66.5°
(ii)

71.5°
(iii)

56.5°
(iv)

86.5°
(v)

61.5°

Question 24

24.

In the given figure, O is the centre of the circle and the tangents BE and DE meet at point E. If ∠CDB = 56°, find ∠BOD

(i)

142°
(ii)

112°
(iii)

117°
(iv)

127°
(v)

122°

Question 25

25.

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

(i)

chord
(ii)

tangent
(iii)

segment
(iv)

secant
(v)

diameter

Question 26

26.

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

(i)

semi-circle
(ii)

tangent
(iii)

diameter
(iv)

circumference
(v)

major segment

Question 27

27.

Which of the following statements are true?

a)	Exactly two tangents can be drawn parallel to a secant.
b)	Only one circle can be drawn with a centre.
c)	Infinite circles can be drawn passing through three collinear points.
d)	Atmost one circle can be drawn passing through three non-collinear points.
e)	Only one circle can be drawn passing through two points.

(i)

{a,d}
(ii)

{b,a}
(iii)

{e,b,a}
(iv)

{c,d}
(v)

{c,d,a}

Question 28

28.

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,d,a}
(ii)

{b,c,a}
(iii)

{d,c}
(iv)

{a,c}
(v)

{b,a}

Question 29

29.

Which of the following statements are true?

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

(i)

{c,e}
(ii)

{d,a,c}
(iii)

{b,e}
(iv)

{a,c}
(v)

{b,e,c}

Question 30

30.

Which of the following statements are true?

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

(i)

{a,b}
(ii)

{b,c,e}
(iii)

{a,b,c}
(iv)

{a,d,e}
(v)

{d,c}

Question 31

31.

Which of the following statements are true?

a)	A line parallel to a tangent is a secant.
b)	Two different tangents can meet at a point on the circle.
c)	If two tangents to a circle intersect, their points of contact with the circle together with their point of intersection form an isosceles triangle.
d)	If two tangents are parallel, the distance between them is equal to the diameter of the circle.
e)	If two tangents are perpendicular, they form a right angled triangle with their points of contact with the circle and their point of intersection.

(i)

{c,d,e}
(ii)

{b,d}
(iii)

{a,c}
(iv)

{a,c,d}
(v)

{a,b,e}

Question 32

32.

Which of the following statements are true?

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

(i)

{a,d}
(ii)

{a,b}
(iii)

{a,c}
(iv)

{a,b,c}
(v)

{b,c,d}

Question 33

33.

Which of the following statements are true?

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

(i)

{d,e}
(ii)

{a,d}
(iii)

{a,e,d}
(iv)

{c,f,d}
(v)

{b,e}

Question 34

34.

With the vertices of a triangle △EFG as centres, three circles are drawn touching each other externally. If the sides of the triangle are 9 cm , 14 cm and 11 cm , find the radii of the circles

(i)

3 cm , 11 cm & 8 cm respectively
(ii)

8 cm , 11 cm & 13 cm respectively
(iii)

8 cm , 6 cm & 8 cm respectively
(iv)

3 cm , 6 cm & 13 cm respectively
(v)

3 cm , 6 cm & 8 cm respectively

Question 35

35.

In the given figure, HI and JK are parallel tangents to the circle with centre O. HK is another tangent meeting HI and JK at H and K. Find ∠HOK

(i)

105°
(ii)

95°
(iii)

100°
(iv)

90°
(v)

120°

Question 36

36.

In the given figure, AD is the common tangent to the two circles. AB & AC are also tangents. Given AB = 11 cm, find AC

(i)

11 cm
(ii)

9 cm
(iii)

12 cm
(iv)

10 cm
(v)

13 cm

Question 37

37.

In the given figure, CP & DP are tangents to the circle with centre O. Given ∠P = 56°, find ∠C

(i)

28°
(ii)

33°
(iii)

38°
(iv)

43°
(v)

58°

Question 38

38.

In the given figure, GS & HS are tangents to the circle with centre O. Given OG = 15 cm and GH = 26 cm, find GS

(i)

24.06 cm
(ii)

25.06 cm
(iii)

26.06 cm
(iv)

27.06 cm
(v)

28.06 cm

Question 39

39.

In the given figure, DP & EP are tangents to the circle with centre O. Given ∠DOE = 124°, find ∠DPE

(i)

86°
(ii)

56°
(iii)

61°
(iv)

71°
(v)

66°

Question 40

40.

Two concentric circles are of radii 18 cm and 8 cm. Find the length of the chord of the outer circle that touches the inner circle

(i)

34.25 cm
(ii)

33.25 cm
(iii)

31.25 cm
(iv)

32.25 cm
(v)

30.25 cm

Assignment Key