EduSahara™ Worksheet

Question 1

1.

O is the centre of the circumcircle of △BCD. Tangents at B and D intersect at E. If ∠BED = 60.3°, find ∠DCB

(i)

59.85°
(ii)

64.85°
(iii)

89.85°
(iv)

69.85°
(v)

74.85°

Question 2

2.

If two circles of radii 10 cm and 6 cm touch internally, the distance between their centres is

(i)

6 cm
(ii)

4 cm
(iii)

5 cm
(iv)

2 cm
(v)

3 cm

Question 3

3.

In the given figure, O is the centre of the circle and HI is the tangent at E. If ∠FEG = 35° and ∠HEF = 41°, find ∠GEI

(i)

119°
(ii)

109°
(iii)

134°
(iv)

114°
(v)

104°

Question 4

4.

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

(i)

2
(ii)

0
(iii)

(-1)
(iv)

4
(v)

1

Question 5

5.

In the given figure, O is the centre of the circle and the tangents CF and EF meet at point F. If ∠DEC = 59°, find ∠EFC

(i)

72°
(ii)

67°
(iii)

77°
(iv)

62°
(v)

92°

Question 6

6.

Which of the following statements are true?

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

(i)

{b,d,e}
(ii)

{d,c}
(iii)

{b,a}
(iv)

{a,c,e}
(v)

{b,a,c}

Question 7

7.

O is the centre of the circumcircle of △IJK. Tangents at I and J intersect at L. If ∠ILJ = 54.77° and ∠IOK = 110°, find ∠KIJ

(i)

67.39°
(ii)

62.39°
(iii)

72.39°
(iv)

92.39°
(v)

77.39°

Question 8

8.

In the given figure, O is the centre of the circle and GH is the tangent at F. If ∠ECF = 63° and ∠CED = 52°, find ∠ECD

(i)

43°
(ii)

48°
(iii)

68°
(iv)

38°
(v)

53°

Question 9

9.

In the given figure, O is the centre of the circle and the tangents IL and KL meet at point L. If ∠JKI = 48°, find ∠IOK

(i)

126°
(ii)

96°
(iii)

106°
(iv)

111°
(v)

101°

Question 10

10.

In the given figure, O is the centre of the circle and EF is the tangent at D. If ∠DCB = 32°, find ∠FDB

(i)

47°
(ii)

32°
(iii)

62°
(iv)

42°
(v)

37°

Question 11

11.

DE is a line segment and G is its mid-point. Three semi-circles are drawn with DG , GE and DE as diameters. F , H and G respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given DF = 6 cm

(i)

4.00 cm
(ii)

3.00 cm
(iii)

2.00 cm
(iv)

6.00 cm
(v)

5.00 cm

Question 12

12.

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)

None of these
(iv)

√

d

2

−

(

r

1

−

r

2

)

2
(v)

√

d

2

+

(

r

1

−

r

2

)

2

Question 13

13.

Which of the following statements are true?

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

(i)

{c,d}
(ii)

{a,d}
(iii)

{c,d,a}
(iv)

{e,b,a}
(v)

{b,a}

Question 14

14.

Which of the following statements are true?

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

(i)

{c,a,b}
(ii)

{a,b,d}
(iii)

{e,b}
(iv)

{c,a}
(v)

{c,e,d}

Question 15

15.

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)

60°
(ii)

85°
(iii)

55°
(iv)

70°
(v)

65°

Question 16

16.

In the given figure, O is the centre of the circle and GI is the tangent at H . If ∠FEH = 26°, find ∠FGH

(i)

43°
(ii)

38°
(iii)

48°
(iv)

53°
(v)

68°

Question 17

17.

Which of the following statements are true?

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

(i)

{b,f}
(ii)

{d,f}
(iii)

{c,e,d}
(iv)

{a,d}
(v)

{a,f,d}

Question 18

18.

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

(i)

{c,a,b}
(ii)

{a,b,d}
(iii)

{c,a}
(iv)

{c,d}
(v)

{c,b}

Question 19

19.

Two circles are of radii 2 cm and 5 cm. If the distance between their centres is 12 cm, what is the length of their direct common tangent?

(i)

12.62 cm
(ii)

13.62 cm
(iii)

11.62 cm
(iv)

9.62 cm
(v)

10.62 cm

Question 20

20.

Which of the following statements are true?

a)	A secant of a circle is a segment having its end points on the circle.
b)	Every circle has a unique diameter.
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)

{c,a,d}
(ii)

{b,e}
(iii)

{b,e,d}
(iv)

{a,d}
(v)

{d,e}

Question 21

21.

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

(i)

3
(ii)

2
(iii)

0
(iv)

4
(v)

6

Question 22

22.

Which of the following statements are true?

a)	A line parallel to a tangent is a secant.
b)	If two tangents are perpendicular, they form a right angled triangle with their points of contact with the circle and their point of intersection.
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)	Two different tangents can meet at a point on the circle.

(i)

{a,b}
(ii)

{a,e,d}
(iii)

{e,c}
(iv)

{b,c,d}
(v)

{a,b,c}

Question 23

23.

In the given figure, DE and FG are parallel tangents to the circle with centre O. DG is another tangent meeting DE and FG at D and G. Find ∠DOG

(i)

100°
(ii)

105°
(iii)

120°
(iv)

95°
(v)

90°

Question 24

24.

In the given figure, O is the centre of the circle and IJ is the tangent at F. If ∠OGF = 38°, find ∠JFG

(i)

57°
(ii)

82°
(iii)

62°
(iv)

67°
(v)

52°

Question 25

25.

In the given figure, O is the centre of the circle and GI is the tangent at H. If ∠FEH = 27°, find ∠FGH + ∠FHG

(i)

63°
(ii)

73°
(iii)

78°
(iv)

68°
(v)

93°

Assignment Key