EduSahara™ Worksheet

Question 1

1.

In the given figure, DE is a diameter of the circle with centre O. If ∠EDF = 28.6° and EF = EG, find ∠GFD

(i)

71.4°
(ii)

76.4°
(iii)

61.4°
(iv)

91.4°
(v)

66.4°

Question 2

2.

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

(i)
F

=

116°

,

G

=

90°

,

H

=

64°

,

I

=

90°
(ii)
F

=

115°

,

G

=

90°

,

H

=

65°

,

I

=

90°
(iii)
F

=

112°

,

G

=

90°

,

H

=

68°

,

I

=

90°
(iv)
F

=

113°

,

G

=

90°

,

H

=

67°

,

I

=

90°
(v)
F

=

114°

,

G

=

90°

,

H

=

66°

,

I

=

90°

Question 3

3.

The radii of the circle are

(i)

RL

,

RM

,

RN

,

RO

,

RP

,

RQ

(ii)

LM

,

MN

,

NO

,

OP

,

PQ

,

QL

,

OQ

(iii)

LM

,

MN

,

NO

,

OP

,

PQ

,

QL

,

RN

(iv)

MN

,

NO

,

OP

,

PQ

,

QL
(v)

LM

,

MN

,

NO

,

OP

,

PQ

,

QL

Question 4

4.

A line segment having its end points on the circle is called a

(i)

major segment
(ii)

circumference
(iii)

centre
(iv)

chord
(v)

radius

Question 5

5.

In the given figure, O is the centre of the circle . If ∠DGE = 80° and ∠DCF = 64°, find ∠CHD

(i)

38°
(ii)

58°
(iii)

43°
(iv)

33°
(v)

28°

Question 6

6.

O is the centre of the circle. If Arc JL = 2 Arc LM and ∠JOL = 100°, find ∠JKL

(i)

130°
(ii)

135°
(iii)

145°
(iv)

160°
(v)

140°

Question 7

7.

In the given figure, DF is a chord which is equal to the radius of the circle. Find ∠G and ∠E

(i)

50° & 130°
(ii)

45° & 135°
(iii)

60° & 120°
(iv)

40° & 140°
(v)

30° & 150°

Question 8

8.

Find the side of the square in the following figure if the radius of the circle is 10.00 cm.

(i)

15.14 cm
(ii)

14.14 cm
(iii)

13.14 cm
(iv)

12.14 cm
(v)

16.14 cm

Question 9

9.

In the given figure, ABCDEF is a regular hexagon inscribed in a circle with centre O. Which of the following are true?

a)	∠FDC = 90°
b)	∠AOF = 60°
c)	∠ACB = 60°
d)	∠BOD = 120°
e)	∠BEC = 30°

(i)

{a,b,d,e}
(ii)

{c,b}
(iii)

{c,a}
(iv)

{c,d}
(v)

{c,e,a}

Question 10

10.

IJKLMN is a hexagon inscribed in a circle. Given ∠IJK = 129° & ∠KLM = 126°, find ∠MNI

(i)

135°
(ii)

105°
(iii)

120°
(iv)

110°
(v)

115°

Question 11

11.

If the radius of a circle is 84 cm, what is its circumference?

(i)

530 cm
(ii)

526 cm
(iii)

527 cm
(iv)

529 cm
(v)

528 cm

Question 12

12.

△GHI is inscribed in a circle with centre O. If ∠GOH = 120° and ∠HOI = 152°, find ∠GHI

(i)

59°
(ii)

44°
(iii)

74°
(iv)

54°
(v)

49°

Question 13

13.

In the given figure, HI & JK are diameters of the circle. If ∠HIJ = 67.5° find, ∠IOJ

(i)

55°
(ii)

75°
(iii)

60°
(iv)

45°
(v)

50°

Question 14

14.

In the given figure, EF ∥ GH. Length of chords EF = 18 cm and GH = 27 cm.

If the distance between the chords is
7 cm
,
find the radius of the circle

(i)

15.01 cm
(ii)

14.01 cm
(iii)

16.01 cm
(iv)

13.01 cm
(v)

12.01 cm

Question 15

15.

In the given figure, a pentagon is inscribed in a circle with centre O. Given CD = DE = EF and ∠CDE = 100°. Find ∠CBD

(i)

40°
(ii)

50°
(iii)

70°
(iv)

45°
(v)

55°

Question 16

16.

In the given figure, which of the following are true?

a)	∠A + ∠OBC = 90°
b)	∠A + ∠OBC + ∠OCB = 2 ∠A
c)	∠A + ∠OCB = 90°
d)	∠A + ∠OBC = 120°
e)	∠A + ∠BOC = 180°

(i)

{e,b,a}
(ii)

{a,c}
(iii)

{b,a}
(iv)

{d,c,a}
(v)

{d,c}

Question 17

17.

In the given figure, O is the centre of the circle. If ∠ODF = 51°, find ∠E

(i)

171°
(ii)

151°
(iii)

146°
(iv)

156°
(v)

141°

Question 18

18.

(i)

94°
(ii)

89°
(iii)

99°
(iv)

84°
(v)

114°

Question 19

19.

Two concentric circles are of radii 17 cm and 13 cm. Find the length of the chord of the outer circle that touches the inner circle

(i)

23.91 cm
(ii)

22.91 cm
(iii)

21.91 cm
(iv)

20.91 cm
(v)

19.91 cm

Question 20

20.

In triangle ABC, if a circle is drawn with BC as diameter and if it passes through A it is a

(i)

acute angled triangle
(ii)

equilateral triangle
(iii)

obtuse angled triangle
(iv)

right angle triangle

Question 21

21.

O is the centre of the circle. If ∠AOB = 67°, find the angle ∠D

(i)

63.5°
(ii)

38.5°
(iii)

48.5°
(iv)

33.5°
(v)

43.5°

Question 22

22.

In the given figure, JK & LM are diameters of the circle. If ∠JML = 42°, find ∠OLK

(i)

47°
(ii)

42°
(iii)

72°
(iv)

52°
(v)

57°

Question 23

23.

In the given figure, IJKL is a cyclic quadrilateral. If ∠IKJ = 37° and ∠KLJ = 48°, find ∠IJK

(i)

110°
(ii)

105°
(iii)

100°
(iv)

125°
(v)

95°

Question 24

24.

O is the centre of the circle and ∠KHJ = 33°, find ∠HIJ

(i)

133°
(ii)

128°
(iii)

123°
(iv)

153°
(v)

138°

Question 25

25.

In the given figure, O is the centre of the circle and HK is a diameter. If ∠JKG = 94° and ∠GHK = 59°, find ∠HIJ

(i)

132°
(ii)

122°
(iii)

127°
(iv)

147°
(v)

117°

Assignment Key