EduSahara™ Worksheet

Question 1

1.

Which of the following figures represent a secant ?

(i)

fig V
(ii)

fig II
(iii)

fig IV
(iv)

fig I
(v)

fig III

Question 2

2.

Find the missing angle in the following figure?

(i)

51°
(ii)

56°
(iii)

76°
(iv)

46°
(v)

61°

Question 3

3.

Two concentric circles are of radii 23 cm and 12 cm. Find the length of the chord of the outer circle that touches the inner circle

(i)

41.24 cm
(ii)

37.24 cm
(iii)

40.24 cm
(iv)

39.24 cm
(v)

38.24 cm

Question 4

4.

In the given figure, BC = 9 cm and AB = 11 cm. Find the perimeter of the shaded region

(i)

78.88 cm
(ii)

75.88 cm
(iii)

73.88 cm
(iv)

81.88 cm
(v)

83.88 cm

Question 5

5.

Which of the following statements are true?

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

(i)

{e,f}
(ii)

{a,f,e}
(iii)

{a,e}
(iv)

{c,d,e}
(v)

{b,f}

Question 6

6.

Points which lie on the circumference of the circle are called

(i)

Concurrent points
(ii)

Concyclic points
(iii)

Cyclic points
(iv)

Similar points
(v)

Coincident points

Question 7

7.

The perimeter of a circle is called

(i)

major segment
(ii)

diameter
(iii)

chord
(iv)

semi-circle
(v)

circumference

Question 8

8.

In the given figure, find the angles of the quadrilateral.

(i)
H

=

110°

,

I

=

90°

,

J

=

70°

,

K

=

90°
(ii)
H

=

112°

,

I

=

90°

,

J

=

68°

,

K

=

90°
(iii)
H

=

111°

,

I

=

90°

,

J

=

69°

,

K

=

90°
(iv)
H

=

109°

,

I

=

90°

,

J

=

71°

,

K

=

90°
(v)
H

=

108°

,

I

=

90°

,

J

=

72°

,

K

=

90°

Question 9

9.

Which of the following statements are true?

a)

All chords of a circle are diameters.

b)

π
is a rational number.

c)

All diameters of a circle are chords.

d)

22
7
is a rational number.

e)

A circle divides the plane into three mutually disjoint sets of points.

(i)

{a,c}
(ii)

{c,d,e}
(iii)

{a,b,e}
(iv)

{a,c,d}
(v)

{b,d}

Question 10

10.

Which of the following statements are true?

a)	The area enclosed by a chord and its major arc is called major segment.
b)	A sector is the area enclosed by two radii and a chord.
c)	The diameter divides the circle into two unequal parts.
d)	The area enclosed by a chord and its minor arc is called minor segment.
e)	A circle divides the plane on which it lies into three parts.

(i)

{c,d}
(ii)

{b,a}
(iii)

{b,a,d}
(iv)

{a,d,e}
(v)

{b,c,e}

Question 11

11.

In the given figure, ABCD is a square with side 20.00 cm. Find the area of the shaded region

(i)

206.57 sq.cm
(ii)

228.57 sq.cm
(iii)

242.57 sq.cm
(iv)

212.57 sq.cm
(v)

255.57 sq.cm

Question 12

12.

Two circles touch internally. J is the centre of the bigger circle and lies on the smaller circle. If ∠GHI = 52°, find ∠G

(i)

68°
(ii)

48°
(iii)

38°
(iv)

43°
(v)

53°

Question 13

13.

In the given triangle S is the circumcentre. If SE = 13.20 cm, find the circumference of the circumcircle

(i)

84.0 cm
(ii)

81.0 cm
(iii)

82.0 cm
(iv)

85.0 cm
(v)

83.0 cm

Question 14

14.

The centre of the circle is

(i)

F
(ii)

D
(iii)

G
(iv)

I
(v)

E

Question 15

15.

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

(i)

tangent
(ii)

radius
(iii)

quadrant
(iv)

segment
(v)

semi-circle

Question 16

16.

In the given figure, BC = 15 cm and AB = 6 cm. Find the area of the shaded region

(i)

174.07 sq.cm
(ii)

157.07 sq.cm
(iii)

137.07 sq.cm
(iv)

160.07 sq.cm
(v)

166.07 sq.cm

Question 17

17.

With the vertices of a triangle △BCD as centres, three circles are drawn touching each other externally. If the sides of the triangle are 10 cm , 15 cm and 15 cm , find the radii of the circles

(i)

5 cm , 10 cm & 10 cm respectively
(ii)

5 cm , 5 cm & 10 cm respectively
(iii)

10 cm , 5 cm & 10 cm respectively
(iv)

10 cm , 10 cm & 15 cm respectively
(v)

5 cm , 5 cm & 15 cm respectively

Question 18

18.

The angle subtended by the semicircle at the centre is

(i)

180°
(ii)

195°
(iii)

210°
(iv)

185°
(v)

190°

Question 19

19.

In the given figure, the circle circumscribes a rectangle with sides 16.00 cm and 14.00 cm. Find the area of the remaining portion other than the rectangle

(i)

143.14 sq.cm
(ii)

147.14 sq.cm
(iii)

117.14 sq.cm
(iv)

131.14 sq.cm
(v)

118.14 sq.cm

Question 20

20.

The major segment of the circle is

(i)

OJLKO
(ii)

JLK
(iii)

OJMKO
(iv)

JMK
(v)

JMKNJ

Question 21

21.

If the diameter of a circle is 56 cm, what is its radius?

(i)

29 cm
(ii)

28 cm
(iii)

26 cm
(iv)

27 cm
(v)

30 cm

Question 22

22.

A line segment joining any point on the circle with its centre is called

(i)

circumference
(ii)

major segment
(iii)

semi-circle
(iv)

diameter
(v)

radius

Question 23

23.

If a chord DE = 14 cm is drawn in a circle with radius OD = 9 cm, find its distance from the centre of the circle

(i)

3.66 cm
(ii)

7.66 cm
(iii)

4.66 cm
(iv)

5.66 cm
(v)

6.66 cm

Question 24

24.

If two circles of radii 10 cm and 2 cm touch internally, the distance between their centres is

(i)

9 cm
(ii)

8 cm
(iii)

7 cm
(iv)

6 cm
(v)

10 cm

Question 25

25.

In the given figure, ABCD is a square of side 12.00 cm and A, B, C, D are centres of circles which touch externally in pairs. Find the area of the shaded region

(i)

475.43 sq.cm
(ii)

483.43 sq.cm
(iii)

499.43 sq.cm
(iv)

468.43 sq.cm
(v)

487.43 sq.cm

Assignment Key