EduSahara™ Worksheet

Question 1

1.

Which of the following figures represent a chord ?

(i)

fig II
(ii)

fig III
(iii)

fig I
(iv)

fig IV
(v)

fig V

Question 2

2.

Half of a circle is called

(i)

major segment
(ii)

segment
(iii)

semi-circle
(iv)

centre
(v)

radius

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 = 43°, find ∠GEI

(i)

107°
(ii)

117°
(iii)

112°
(iv)

102°
(v)

132°

Question 4

4.

If the radius of the circumcircle is half the length of a side of the triangle, then the triangle is

(i)

right angle triangle
(ii)

acute angled triangle
(iii)

obtuse angled triangle
(iv)

equilateral triangle

Question 5

5.

In the given figure, O is the centre of the circle and LM is the tangent at H. If ∠HKJ = 53°, find ∠MHJ

(i)

58°
(ii)

68°
(iii)

53°
(iv)

83°
(v)

63°

Question 6

6.

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 = 61°, find ∠EFG

(i)

71°
(ii)

76°
(iii)

91°
(iv)

66°
(v)

61°

Question 7

7.

Which of the following statements are true?

a)	Angles subtended by equal length arcs in two circles are equal.
b)	Angles in the same segment are equal.
c)	Angles in the opposite segments are supplementary.
d)	Angles in the opposite segments are complementary.

(i)

{a,c,b}
(ii)

{d,c}
(iii)

{a,d,b}
(iv)

{a,b}
(v)

{b,c}

Question 8

8.

The angle subtended by the diameter at any point on the circle is

(i)

120°
(ii)

90°
(iii)

100°
(iv)

105°
(v)

95°

Question 9

9.

If two circles of radii 8 cm and 5 cm touch internally, the distance between their centres is

(i)

2 cm
(ii)

3 cm
(iii)

1 cm
(iv)

5 cm
(v)

4 cm

Question 10

10.

In the given figure, CS & DS are tangents to the circle with centre O. Given ∠S = 48°, find ∠C

(i)

34°
(ii)

29°
(iii)

54°
(iv)

39°
(v)

24°

Question 11

11.

Which of the following statements are true?

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

(i)

{c,d}
(ii)

{b,c,e}
(iii)

{a,d,e}
(iv)

{b,a,d}
(v)

{b,a}

Question 12

12.

A chord of a circle divides the whole circular region into two parts, each called a

(i)

circumference
(ii)

chord
(iii)

segment
(iv)

diameter
(v)

semi-circle

Question 13

13.

In the given figure, O is the centre of the circle and FH is the tangent at G. If ∠GHI = 36°,∠HGI = 35°, find ∠JGI

(i)

104°
(ii)

89°
(iii)

79°
(iv)

74°
(v)

84°

Question 14

14.

In the given figure, O is the centre of the circle and BD is the tangent at C. If ∠CDE = 47°,∠DCE = 31°, find ∠GCB

(i)

108°
(ii)

88°
(iii)

83°
(iv)

93°
(v)

78°

Question 15

15.

The segment of the circle containing the centre of the circle is called

(i)

segment
(ii)

chord
(iii)

diameter
(iv)

semi-circle
(v)

major segment

Question 16

16.

Which of the following statements are true?

a)	A cyclic quadrilateral is a regular polygon.
b)	If a kite is cyclic, it is a square.
c)	If a parallelogram is cyclic, it is a rectangle.
d)	If a trapezium is cyclic, it is a rectangle.
e)	If a rhombus is cyclic, it is a square.

(i)

{d,a,c}
(ii)

{c,e}
(iii)

{b,e}
(iv)

{a,c}
(v)

{b,e,c}

Question 17

17.

In the given figure, DP & EP are tangents to the circle with centre O. Given OD = 12 cm and DE = 21 cm, find DP

(i)

23.69 cm
(ii)

19.69 cm
(iii)

22.69 cm
(iv)

20.69 cm
(v)

21.69 cm

Question 18

18.

FG is a line segment and I is its mid-point. Three semi-circles are drawn with FI , IG and FG as diameters. H , J and I respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given FH = 5 cm

(i)

5.33 cm
(ii)

3.33 cm
(iii)

4.33 cm
(iv)

1.33 cm
(v)

2.33 cm

Question 19

19.

In triangle FGH, if a circle is drawn with GH as diameter and if it passes through F it is a

(i)

right angle triangle
(ii)

equilateral triangle
(iii)

obtuse angled triangle
(iv)

acute angled triangle

Question 20

20.

O is the centre of the circle. HI and JI are tangents to the circle. If ∠JKH = 50°, find ∠HIJ

(i)

80°
(ii)

110°
(iii)

90°
(iv)

85°
(v)

95°

Question 21

21.

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

(i)

120°
(ii)

100°
(iii)

105°
(iv)

90°
(v)

95°

Question 22

22.

In the given figure, O is the centre of the circle and IK is the tangent at J . If ∠HGJ = 30°, find ∠HIJ

(i)

60°
(ii)

40°
(iii)

30°
(iv)

35°
(v)

45°

Question 23

23.

Which of the following figures represent a tangent ?

(i)

fig IV
(ii)

fig III
(iii)

fig V
(iv)

fig II
(v)

fig I

Question 24

24.

Two circles are of radii 4 cm and 5 cm. If the distance between their centres is 15 cm, what is the length of their transverse common tangent?

(i)

12.00 cm
(ii)

10.00 cm
(iii)

13.00 cm
(iv)

11.00 cm
(v)

14.00 cm

Question 25

25.

In the given figure, O is the centre of the circle and LM is the tangent at I. If ∠OJI = 30.5°, find ∠MIJ

(i)

74.5°
(ii)

89.5°
(iii)

59.5°
(iv)

69.5°
(v)

64.5°

Assignment Key