EduSahara™ Worksheet

Question 1

1.

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

(i)

major segment
(ii)

centre
(iii)

segment
(iv)

circumference
(v)

chord

Question 2

2.

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)

radius
(ii)

centre
(iii)

quadrant
(iv)

secant
(v)

major segment

Question 3

3.

In the given figure , ABCD is a trapezium. A quarter circle AEFD is removed from the trapezium. If AD = CD = 11 and EB = 3.3 , find the area of the remaining portion

(i)

44.08 sq.cm
(ii)

41.08 sq.cm
(iii)

39.08 sq.cm
(iv)

47.08 sq.cm
(v)

49.08 sq.cm

Question 4

4.

Two circles touch internally. E is the centre of the bigger circle and lies on the smaller circle. If ∠BCD = 65°, find ∠B

(i)

55°
(ii)

25°
(iii)

35°
(iv)

40°
(v)

30°

Question 5

5.

In the given figure, the radius of the circle is 15 cm. Find the area of the minor sector

(i)

192.78 sq.cm
(ii)

149.78 sq.cm
(iii)

158.78 sq.cm
(iv)

199.78 sq.cm
(v)

176.78 sq.cm

Question 6

6.

The angle subtended by the semicircle at the centre is

(i)

190°
(ii)

180°
(iii)

185°
(iv)

210°
(v)

195°

Question 7

7.

A chord that passes through the centre of the circle is called

(i)

diameter
(ii)

centre
(iii)

circumference
(iv)

radius
(v)

major segment

Question 8

8.

In the given figure, O is the centre of the circle and CE is the tangent at D. If ∠BAD = 27°, find ∠BCD + ∠BDC

(i)

78°
(ii)

68°
(iii)

63°
(iv)

73°
(v)

93°

Question 9

9.

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)	If two tangents are parallel, the distance between them is equal to the diameter of the circle.
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)	A line parallel to a tangent is a secant.
e)	Two different tangents can meet at a point on the circle.

(i)

{e,b}
(ii)

{d,a}
(iii)

{d,e,c}
(iv)

{a,b,c}
(v)

{d,a,b}

Question 10

10.

The given figure consists of four small semi-circles of equal radii and two big semi-circles of equal radii. The radius of each big semi-circle is 6.00 cm which is the same as the diameter of the small semi-circle. Find the area of the shaded region

(i)

98.14 sq.cm
(ii)

127.14 sq.cm
(iii)

135.14 sq.cm
(iv)

113.14 sq.cm
(v)

87.14 sq.cm

Question 11

11.

In the given figure, O is the centre of the circle. G is a point on chord EF such that EG = GF. Find ∠OGE

(i)

105°
(ii)

100°
(iii)

90°
(iv)

95°
(v)

120°

Question 12

12.

In the given figure, ABCD is a square of side 19.00 cm and A, B, C, D are the centres of circular arcs, each of radius 9.50 cm. Find the area of the shaded region

(i)

80.36 sq.cm
(ii)

74.36 sq.cm
(iii)

72.36 sq.cm
(iv)

82.36 sq.cm
(v)

77.36 sq.cm

Question 13

13.

Which of the following figures represent a diameter ?

(i)

fig V
(ii)

fig III
(iii)

fig I
(iv)

fig II
(v)

fig IV

Question 14

14.

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)	An infinite number of diameters may be drawn for a circle.
d)	One and only one tangent can be drawn to a circle from a point outside it.
e)	Every circle has a unique diameter.

(i)

{a,b,c}
(ii)

{d,a,b}
(iii)

{e,b}
(iv)

{d,a}
(v)

{d,e,c}

Question 15

15.

'O' is the centre of a circle of radius 'r' and 'P' is any point in its plane.
If
OP
< r,then P is

(i)

outside the circle
(ii)

on the circle
(iii)

inside the circle

Question 16

16.

The point of intersection of the angular bisectors of a triangle is

(i)

centroid
(ii)

excentre
(iii)

circumcentre
(iv)

incentre
(v)

orthocentre

Question 17

17.

In the given figure ,PQRS is the diameter of the circle of radius 9.00 cm and PQ = QR = RS. Find the area of the shaded region

(i)

164.71 sq.cm
(ii)

169.71 sq.cm
(iii)

155.71 sq.cm
(iv)

181.71 sq.cm
(v)

172.71 sq.cm

Question 18

18.

O is the centre of the circumcircle of △IJK. Tangents at I and K intersect at L. If ∠ILK = 50.41°, find ∠KJI

(i)

94.8°
(ii)

69.8°
(iii)

79.8°
(iv)

74.8°
(v)

64.8°

Question 19

19.

'O' is the centre of a circle of radius 'r' and 'P' is any point in its plane.
If
OP
> r,then P is

(i)

outside the circle
(ii)

on the circle
(iii)

inside the circle

Question 20

20.

With the vertices of a triangle △FGH as centres, three circles are drawn touching each other externally. If the sides of the triangle are 10 cm , 18 cm and 12 cm , find the radii of the circles

(i)

7 cm , 13 cm & 15 cm respectively
(ii)

2 cm , 8 cm & 15 cm respectively
(iii)

7 cm , 8 cm & 10 cm respectively
(iv)

2 cm , 13 cm & 10 cm respectively
(v)

2 cm , 8 cm & 10 cm respectively

Question 21

21.

In the given figure, O is the centre of the circle and LM is the tangent at I. If ∠JIK = 58° and ∠LIJ = 48°, find ∠KIM

(i)

79°
(ii)

74°
(iii)

89°
(iv)

104°
(v)

84°

Question 22

22.

In the given figure, O is the centre of the circle and JK is the tangent at I. If ∠IHG = 37°, find ∠KIG

(i)

67°
(ii)

37°
(iii)

47°
(iv)

52°
(v)

42°

Question 23

23.

In the given figure, O is the centre of the circle and KL is the tangent at J. If ∠IGJ = 30° and ∠GIH = 44°, find ∠IGH

(i)

51°
(ii)

76°
(iii)

61°
(iv)

56°
(v)

46°

Question 24

24.

In the given figure, O is the centre of the circle and JK is the tangent at G. If ∠OHG = 32°, find ∠KGH

(i)

58°
(ii)

63°
(iii)

73°
(iv)

68°
(v)

88°

Question 25

25.

If two circles are concentric, then

(i)

their radii are same
(ii)

their centres are same
(iii)

their diameters are same
(iv)

their perimeters are same

Assignment Key