EduSahara™ Worksheet

Question 1

1.

O is the centre of the circumcircle of △FGH. Tangents at F and H intersect at I. If ∠FIH = 50.46°, find ∠HGF

(i)

74.77°
(ii)

79.77°
(iii)

94.77°
(iv)

69.77°
(v)

64.77°

Question 2

2.

In the given figure, O is the centre of the circle and EF is the tangent at D. If ∠CAD = 55° and ∠ACB = 61°, find ∠FDA

(i)

50°
(ii)

35°
(iii)

65°
(iv)

40°
(v)

45°

Question 3

3.

In the given figure, two circles intersect at points J & K. A tangent is drawn at point L. From the same point, two lines are drawn passing through points J & K. They meet the other end of the second circle at I & H. Given ∠L = 64°, find ∠HKJ

(i)

116°
(ii)

131°
(iii)

126°
(iv)

146°
(v)

121°

Question 4

4.

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

(i)

diameter
(ii)

tangent
(iii)

circumference
(iv)

centre
(v)

major segment

Question 5

5.

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

(i)

6 cm
(ii)

5 cm
(iii)

7 cm
(iv)

3 cm
(v)

4 cm

Question 6

6.

In the given figure, O is the centre of the circle and GH is the tangent at F. If ∠ECF = 59° and ∠CED = 61°, find ∠GFE

(i)

89°
(ii)

69°
(iii)

74°
(iv)

59°
(v)

64°

Question 7

7.

In the given figure, O is the centre of the circle and HI is the tangent at D. If ∠DGF = 49°, find ∠DEF

(i)

141°
(ii)

146°
(iii)

136°
(iv)

161°
(v)

131°

Question 8

8.

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)

major segment
(iii)

quadrant
(iv)

tangent
(v)

semi-circle

Question 9

9.

Two circles with equal radii are

(i)

only similar but not congruent
(ii)

concentric
(iii)

congruent
(iv)

not similar

Question 10

10.

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

(i)

100°
(ii)

120°
(iii)

95°
(iv)

105°
(v)

90°

Question 11

11.

In the given figure, DB and DC are tangent segments to the circle with centre O. Given ∠CDE = 31°, find ∠BCE

(i)

59.5°
(ii)

34.5°
(iii)

39.5°
(iv)

29.5°
(v)

44.5°

Question 12

12.

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

(i)

2
(ii)

1
(iii)

3
(iv)

(-1)
(v)

0

Question 13

13.

O is the centre of the circumcircle of △ABC. Tangents at A and B intersect at D. If ∠ADB = 64.72° and ∠AOC = 130°, find ∠CAB

(i)

57.36°
(ii)

87.36°
(iii)

72.36°
(iv)

62.36°
(v)

67.36°

Question 14

14.

Which of the following statements are true?

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

(i)

{a,b,c}
(ii)

{b,c,d}
(iii)

{e,c}
(iv)

{a,b}
(v)

{a,e,d}

Question 15

15.

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

(i)

2
(ii)

5
(iii)

3
(iv)

1
(v)

4

Question 16

16.

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 17

17.

In the given figure, O is the centre of the circle and the tangents FI and HI meet at point I. If ∠GHF = 53°, find ∠HIF

(i)

84°
(ii)

89°
(iii)

104°
(iv)

74°
(v)

79°

Question 18

18.

In the given figure, O is the centre of the circle and JK is the tangent at G. If ∠OHG = 37.5°, find ∠KGH

(i)

62.5°
(ii)

52.5°
(iii)

82.5°
(iv)

57.5°
(v)

67.5°

Question 19

19.

In the given figure, two circles intersect at points G & H. A tangent is drawn at point I. From the same point, two lines are drawn passing through points G & H. They meet the other end of the second circle at F & E. Given ∠I = 90°, find ∠FEH

(i)

100°
(ii)

90°
(iii)

95°
(iv)

120°
(v)

105°

Question 20

20.

In the given figure, JM is the common tangent to the two circles. JK & JL are also tangents. Given JK = 13 cm, find JL

(i)

14 cm
(ii)

15 cm
(iii)

12 cm
(iv)

13 cm
(v)

11 cm

Question 21

21.

In the given figure, O is the centre of the circle and HI is the tangent at G. If ∠GFE = 30°, find ∠IGE

(i)

35°
(ii)

30°
(iii)

40°
(iv)

45°
(v)

60°

Question 22

22.

In the given figure, BC and DE are parallel tangents to the circle with centre O. BE is another tangent meeting BC and DE at B and E. Find ∠BOE

(i)

100°
(ii)

120°
(iii)

90°
(iv)

105°
(v)

95°

Question 23

23.

Which of the following statements are true?

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

(i)

{d,c,a}
(ii)

{b,a}
(iii)

{e,b,a}
(iv)

{a,c}
(v)

{d,c}

Question 24

24.

Two circles are of radii 5 cm and 3 cm. If the distance between their centres is 12 cm, what is the length of their direct common tangent?

(i)

13.83 cm
(ii)

12.83 cm
(iii)

9.83 cm
(iv)

10.83 cm
(v)

11.83 cm

Question 25

25.

In the given figure, O is the centre of the circle and MN is the tangent at I. If ∠ILK = 50°, find ∠NIK

(i)

60°
(ii)

55°
(iii)

65°
(iv)

80°
(v)

50°

Assignment Key