EduSahara™ Worksheet

Question 1

1.

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 = 59°, find ∠DEF

(i)

69°
(ii)

89°
(iii)

59°
(iv)

64°
(v)

74°

Question 2

2.

In the given figure, O is the centre of the circle and EF is the tangent at D. If ∠CAD = 36° and ∠ACB = 53°, find ∠CAB

(i)

52°
(ii)

67°
(iii)

37°
(iv)

47°
(v)

42°

Question 3

3.

In the given figure, two circles intersect at points C & D. A tangent is drawn at point E. From the same point, two lines are drawn passing through points C & D. They meet the other end of the second circle at B & A. Given ∠E = 80°, find ∠BCD

(i)

115°
(ii)

110°
(iii)

105°
(iv)

130°
(v)

100°

Question 4

4.

In the given figure, BQ & CQ are tangents to the circle with centre O. Given OB = 11 cm and BC = 20 cm, find BQ

(i)

26.00 cm
(ii)

25.00 cm
(iii)

22.00 cm
(iv)

23.00 cm
(v)

24.00 cm

Question 5

5.

In the given figure, GH and IJ are parallel tangents to the circle with centre O. GJ is another tangent meeting GH and IJ at G and J. Find ∠GOJ

(i)

120°
(ii)

90°
(iii)

95°
(iv)

105°
(v)

100°

Question 6

6.

In the given figure, O is the centre of the circle and KL is the tangent at H. If ∠JHI = 54° and ∠IHL = 35°, find ∠JIH

(i)

101°
(ii)

106°
(iii)

91°
(iv)

96°
(v)

121°

Question 7

7.

In the given figure, O is the centre of the circle and DF is the tangent at E. If ∠EFG = 46°,∠FEG = 31°, find ∠HEG

(i)

82°
(ii)

102°
(iii)

77°
(iv)

87°
(v)

72°

Question 8

8.

If two circles of radii 11 cm and 6 cm touch externally, the distance between their centres is

(i)

16 cm
(ii)

19 cm
(iii)

18 cm
(iv)

17 cm
(v)

15 cm

Question 9

9.

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 = 90°, find ∠JIL

(i)

90°
(ii)

120°
(iii)

95°
(iv)

105°
(v)

100°

Question 10

10.

In the given figure, O is the centre of the circle and EF is the tangent at B. If ∠CBD = 52° and ∠EBC = 96°, find ∠BDC

(i)

59°
(ii)

54°
(iii)

44°
(iv)

49°
(v)

74°

Question 11

11.

In the given figure, CR & DR are tangents to the circle with centre O. Given ∠CRD = 61°, find ∠COD

(i)

149°
(ii)

124°
(iii)

119°
(iv)

134°
(v)

129°

Question 12

12.

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

(i)

90°
(ii)

120°
(iii)

95°
(iv)

105°
(v)

100°

Question 13

13.

Two circles with equal radii are

(i)

only similar but not congruent
(ii)

not similar
(iii)

congruent
(iv)

concentric

Question 14

14.

In the given figure, O is the centre of the circle and KM is the tangent at L . If ∠JIL = 27°, find ∠JKL

(i)

51°
(ii)

46°
(iii)

66°
(iv)

36°
(v)

41°

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)	A maximum of four common tangents can be drawn touching any two circles.
c)	Atmost one common tangent can be drawn for any two concentric circles.
d)	Atmost two common tangents can be drawn touching any two circles.

(i)

{d,b}
(ii)

{c,d,a}
(iii)

{a,b}
(iv)

{c,a}
(v)

{c,b,a}

Question 16

16.

In the given figure, O is the centre of the circle and HI is the tangent at D. If ∠DGF = 47°, find ∠DEF

(i)

133°
(ii)

163°
(iii)

138°
(iv)

143°
(v)

148°

Question 17

17.

O is the centre of the circle. CD and ED are tangents to the circle. If ∠EFC = 32°, find ∠CDE

(i)

126°
(ii)

121°
(iii)

131°
(iv)

116°
(v)

146°

Question 18

18.

In the given figure, O is the centre of the circle and HI is the tangent at G. If ∠GFE = 33°, find ∠IGE

(i)

38°
(ii)

63°
(iii)

33°
(iv)

43°
(v)

48°

Question 19

19.

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

(i)

tangent
(ii)

secant
(iii)

segment
(iv)

circumference
(v)

major segment

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)

d

=

√

(

l

2

+

r

2

)
(ii)

l

=

√

(

d

2

+

r

2

)
(iii)

l

=

√

(

d

2

−

r

2

)
(iv)

r

=

√

(

l

2

+

d

2

)
(v)

d

=

√

(

l

2

−

r

2

)

Question 21

21.

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

(i)

69°
(ii)

94°
(iii)

64°
(iv)

74°
(v)

79°

Question 22

22.

In the given figure, GHIJ is a cyclic quadrilateral such that IG bisects ∠JGH and KL is the tangent at I. If ∠IGH = 52°, find ∠KIH

(i)

67°
(ii)

52°
(iii)

62°
(iv)

82°
(v)

57°

Question 23

23.

Which of the following statements are true?

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

(i)

{d,a,c}
(ii)

{a,c}
(iii)

{c,e}
(iv)

{b,e}
(v)

{b,e,c}

Question 24

24.

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

(i)

1
(ii)

0
(iii)

3
(iv)

5
(v)

2

Question 25

25.

With the vertices of a triangle △ABC as centres, three circles are drawn touching each other externally. If the sides of the triangle are 8 cm , 16 cm and 12 cm , find the radii of the circles

(i)

7 cm , 11 cm & 15 cm respectively
(ii)

2 cm , 6 cm & 15 cm respectively
(iii)

7 cm , 6 cm & 10 cm respectively
(iv)

2 cm , 11 cm & 10 cm respectively
(v)

2 cm , 6 cm & 10 cm respectively

Assignment Key