EduSahara™ Worksheet

Question 1

1.

In the given figure, O is the centre of the circle and JK is the tangent at I. If ∠HFI = 53° and ∠FHG = 52°, find ∠KIF

(i)

67°
(ii)

47°
(iii)

42°
(iv)

37°
(v)

52°

Question 2

2.

Two circles are of radii 3 cm and 6 cm. If the distance between their centres is 13 cm, what is the length of their transverse common tangent?

(i)

8.38 cm
(ii)

9.38 cm
(iii)

10.38 cm
(iv)

11.38 cm
(v)

7.38 cm

Question 3

3.

In the given figure, GQ & HQ are tangents to the circle with centre O. Given ∠GOH = 126°, find ∠GQH

(i)

54°
(ii)

69°
(iii)

59°
(iv)

84°
(v)

64°

Question 4

4.

In the given figure, O is the centre of the circle and EF is the tangent at D. If ∠DBC = 42°, find ∠EDC

(i)

57°
(ii)

42°
(iii)

47°
(iv)

52°
(v)

72°

Question 5

5.

In the given figure, IG and IH are tangent segments to the circle with centre O. Given ∠HIJ = 26°, find ∠GHO

(i)

26°
(ii)

31°
(iii)

41°
(iv)

36°
(v)

56°

Question 6

6.

In the given figure, O is the centre of the circle and JK is the tangent at I. If ∠IHG = 45°, find ∠KIG

(i)

50°
(ii)

55°
(iii)

75°
(iv)

60°
(v)

45°

Question 7

7.

In the given figure, O is the centre of the circle and FG is the tangent at E. If ∠DBE = 63° and ∠BDC = 44°, find ∠FED

(i)

93°
(ii)

78°
(iii)

73°
(iv)

68°
(v)

63°

Question 8

8.

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

(i)

4
(ii)

2
(iii)

3
(iv)

6
(v)

1

Question 9

9.

In the given figure, O is the centre of the circle and HI is the tangent at E. If ∠GEF = 60° and ∠FEI = 40°, find ∠GFE

(i)

80°
(ii)

90°
(iii)

110°
(iv)

95°
(v)

85°

Question 10

10.

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)

120°
(ii)

100°
(iii)

95°
(iv)

90°
(v)

105°

Question 11

11.

Which of the following statements are true?

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

(i)

{b,a}
(ii)

{d,c}
(iii)

{b,c,a}
(iv)

{a,c}
(v)

{b,d,a}

Question 12

12.

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

(i)

3
(ii)

5
(iii)

2
(iv)

0
(v)

1

Question 13

13.

Which of the following statements are true?

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

(i)

{c,e,a}
(ii)

{c,e}
(iii)

{a,e}
(iv)

{d,b,a}
(v)

{b,a}

Question 14

14.

In the given figure, CA and CB are tangent segments to the circle with centre O. Given ∠BCD = 36°, find ∠ABD

(i)

57°
(ii)

27°
(iii)

32°
(iv)

42°
(v)

37°

Question 15

15.

If two circles of radii 8 cm and 3 cm touch externally, the distance between their centres is

(i)

9 cm
(ii)

11 cm
(iii)

13 cm
(iv)

12 cm
(v)

10 cm

Question 16

16.

In the given figure, O is the centre of the circle and BD is the tangent at C. If ∠CDE = 53°,∠DCE = 30°, find ∠FCE

(i)

82°
(ii)

77°
(iii)

97°
(iv)

67°
(v)

72°

Question 17

17.

In the given figure, O is the centre of the circle and MN is the tangent at J. If ∠KJL = 47° and ∠MJK = 92°, find ∠JLK

(i)

55°
(ii)

50°
(iii)

60°
(iv)

45°
(v)

75°

Question 18

18.

In the given figure, DEFG is a cyclic quadrilateral such that FD bisects ∠GDE and HI is the tangent at F. If ∠FDE = 56°, find ∠HFE

(i)

66°
(ii)

61°
(iii)

86°
(iv)

71°
(v)

56°

Question 19

19.

Which of the following statements are true?

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

(i)

{d,b}
(ii)

{c,d,e}
(iii)

{c,a,b}
(iv)

{a,b,e}
(v)

{c,a}

Question 20

20.

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

(i)

diameter
(ii)

semi-circle
(iii)

circumference
(iv)

major segment
(v)

tangent

Question 21

21.

If two circles of radii 12 cm and 4 cm touch internally, the distance between their centres is

(i)

7 cm
(ii)

10 cm
(iii)

6 cm
(iv)

8 cm
(v)

9 cm

Question 22

22.

In the given figure, AD is the common tangent to the two circles. AB & AC are also tangents. Given AB = 23 cm, find AC

(i)

21 cm
(ii)

25 cm
(iii)

23 cm
(iv)

22 cm
(v)

24 cm

Question 23

23.

In the given figure, two circles intersect at points I & J. A tangent is drawn at point K. From the same point, two lines are drawn passing through points I & J. They meet the other end of the second circle at H & G. Given ∠K = 52°, find ∠GHI

(i)

57°
(ii)

62°
(iii)

52°
(iv)

67°
(v)

82°

Question 24

24.

Which of the following statements are true?

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

(i)

{c,a,b}
(ii)

{c,e,d}
(iii)

{a,b,d}
(iv)

{c,a}
(v)

{e,b}

Question 25

25.

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)

centre
(iii)

chord
(iv)

circumference
(v)

quadrant

Assignment Key