EduSahara™ Worksheet

Question 1

1.

(i)

145°
(ii)

140°
(iii)

170°
(iv)

155°
(v)

150°

Question 2

2.

O is the centre of the circle. If ∠KOM = 134°, find ∠J

(i)

77°
(ii)

97°
(iii)

72°
(iv)

67°
(v)

82°

Question 3

3.

O is the centre of the circle. If ∠GOF = 143° and ∠HOF = 102°, find ∠GFH

(i)

87.5°
(ii)

62.5°
(iii)

57.5°
(iv)

67.5°
(v)

72.5°

Question 4

4.

Find the missing angle in the following figure?

(i)

39°
(ii)

44°
(iii)

59°
(iv)

34°
(v)

29°

Question 5

5.

O is the centre of the circle and OI = HI. Find ∠HOI

(i)

70°
(ii)

90°
(iii)

65°
(iv)

60°
(v)

75°

Question 6

6.

O is the centre of the circle and OF = EF. Find ∠FOD

(i)

120°
(ii)

135°
(iii)

130°
(iv)

125°
(v)

150°

Question 7

7.

O is the centre of the circle and OD = CD. Find reflex ∠DOB

(i)

270°
(ii)

255°
(iii)

245°
(iv)

240°
(v)

250°

Question 8

8.

Find the side of the square in the following figure if the radius of the circle is 19.00 cm.

(i)

24.87 cm
(ii)

28.87 cm
(iii)

26.87 cm
(iv)

27.87 cm
(v)

25.87 cm

Question 9

9.

(i)

71°
(ii)

86°
(iii)

56°
(iv)

66°
(v)

61°

Question 10

10.

O is the centre of the circle. If ∠GIH = 54° and ∠IGJ = 54°, find t°, u°

(i)

36°, 36°
(ii)

66°, 56°
(iii)

46°, 46°
(iv)

26°, 36°

Question 11

11.

O is the centre of the circle. If ∠DOE = 109°, find the angle ∠F

(i)

84.5°
(ii)

54.5°
(iii)

59.5°
(iv)

69.5°
(v)

64.5°

Question 12

12.

Two circles touch internally. G is the centre of the bigger circle and lies on the smaller circle. If ∠DEF = 53°, find ∠D

(i)

67°
(ii)

37°
(iii)

42°
(iv)

47°
(v)

52°

Question 13

13.

'H' and 'I' are centres of circles of radii 3 cm and 5 cm such that HI = 10 cm and 'J' is the centre of the circle of radius 'r' cm which touches the above circles externally. If ∠HJI = 90°, find 'r'

(i)

3 cm
(ii)

4 cm
(iii)

5 cm
(iv)

2 cm
(v)

1 cm

Question 14

14.

△GHI is inscribed in a circle with centre O. If ∠GOH = 126° and ∠HOI = 150°, find ∠IGH

(i)

90°
(ii)

85°
(iii)

75°
(iv)

105°
(v)

80°

Question 15

15.

△DEF is inscribed in a circle with centre O. If ∠DOE = 106° and ∠EOF = 145°, find ∠DEF

(i)

54.5°
(ii)

64.5°
(iii)

69.5°
(iv)

84.5°
(v)

59.5°

Question 16

16.

△HIJ is inscribed in a circle with centre O. If ∠HOI = 142° and ∠IOJ = 159°, find ∠IJH

(i)

86°
(ii)

101°
(iii)

81°
(iv)

71°
(v)

76°

Question 17

17.

O is the centre of the circle. If ∠HIJ = 118°, find ∠JOK

(i)

66°
(ii)

56°
(iii)

71°
(iv)

61°
(v)

86°

Question 18

18.

O is the centre of the circle and ∠FCE = 32°, find ∠CDE

(i)

137°
(ii)

132°
(iii)

122°
(iv)

127°
(v)

152°

Question 19

19.

O is the centre of the circle. If ∠CAD = 34° and ∠ACB = 25°, find ∠BAC

(i)

61°
(ii)

41°
(iii)

46°
(iv)

36°
(v)

31°

Question 20

20.

In the given figure, O is the centre of the circle and CF is a diameter. If ∠CFG = 58° and ∠DFE = 32°, find ∠FCE

(i)

56°
(ii)

41°
(iii)

26°
(iv)

31°
(v)

36°

Question 21

21.

In the given figure, O is the centre of the circle and chord GH is equal to chord HI and HK is a diameter. If ∠GKH = 35°, find ∠KJI

(i)

125°
(ii)

130°
(iii)

135°
(iv)

140°
(v)

155°

Question 22

22.

In the given figure, O is the centre of the circle and chord GH is equal to chord HI and HK is a diameter. If ∠KGO = 22° and ∠IJK = 112°, find ∠GHI

(i)

146°
(ii)

151°
(iii)

136°
(iv)

141°
(v)

166°

Question 23

23.

In the given figure, O is the centre of the circle , chord FG is equal to chord GH and EG is a diameter. If ∠HEG = 44° find ∠FGH

(i)

92°
(ii)

102°
(iii)

122°
(iv)

97°
(v)

107°

Question 24

24.

In the given figure, O is the centre of the circle , chord CF is equal to chord FE. If ∠COD = 62° and ∠CFE = 102°, find ∠DEF

(i)

75°
(ii)

80°
(iii)

70°
(iv)

85°
(v)

100°

Question 25

25.

In the given figure, O is the centre of the circle. If ∠EOF = 67° and ∠FGI = 72°, find ∠HEO

(i)

15.5°
(ii)

30.5°
(iii)

25.5°
(iv)

45.5°
(v)

20.5°

Question 26

26.

In the given figure, O is the centre of the circle. If ∠FOG = 71° and ∠GHJ = 106°, find ∠IFO

(i)

61.5°
(ii)

56.5°
(iii)

66.5°
(iv)

51.5°
(v)

81.5°

Question 27

27.

In the given figure, O is the centre of the circle. If ∠CFD = 44° and ∠OCF = 21°, find ∠EDF

(i)

141°
(ii)

111°
(iii)

116°
(iv)

126°
(v)

121°

Question 28

28.

In the given figure, O is the centre of the circle. If ∠JHI = 53° and ∠FGJ = 93°, find ∠HJI

(i)

39°
(ii)

34°
(iii)

49°
(iv)

64°
(v)

44°

Question 29

29.

In the given figure, O is the centre of the circle. If ∠DEH = 86°, find ∠FGH

(i)

116°
(ii)

101°
(iii)

96°
(iv)

91°
(v)

86°

Question 30

30.

In the given figure, O is the centre of the circle. If ∠FGD = 81°, find ∠DEF

(i)

109°
(ii)

114°
(iii)

99°
(iv)

104°
(v)

129°

Question 31

31.

In the given figure, O is the centre of the circle and GJ is a diameter. If ∠IJF = 88° and ∠FGJ = 64°, find ∠GHI

(i)

133°
(ii)

128°
(iii)

148°
(iv)

118°
(v)

123°

Question 32

32.

In the given figure, O is the centre of the circle and FG is a diameter. If ∠GOI = 88°, find ∠FHI

(i)

76°
(ii)

61°
(iii)

51°
(iv)

46°
(v)

56°

Question 33

33.

In the given figure, O is the centre of the circle and JM is a diameter. If ∠KLM = 122°, find ∠KIJ

(i)

37°
(ii)

42°
(iii)

32°
(iv)

47°
(v)

62°

Question 34

34.

In the given figure, O is the centre of the circle and EG is a diameter. If ∠FDE = 63°, find ∠FEG

(i)

42°
(ii)

57°
(iii)

32°
(iv)

27°
(v)

37°

Question 35

35.

In the given figure, O is the centre of the circle and GI is a diameter. If ∠FOI = 95° and ∠OIH = 64°, find ∠GHF + ∠HGI

(i)

83.5°
(ii)

68.5°
(iii)

98.5°
(iv)

73.5°
(v)

78.5°

Question 36

36.

In the given figure, O is the centre of the circle and KM is a diameter. If ∠JLK = 26° and ∠KJL = 61°, find ∠MKL + ∠JLM

(i)

108°
(ii)

93°
(iii)

103°
(iv)

98°
(v)

123°

Question 37

37.

In the given figure, O is the centre of the circle. If ∠DEF = 124°, find ∠FOD + ∠DCF

(i)

334°
(ii)

319°
(iii)

314°
(iv)

304°
(v)

309°

Question 38

38.

In the given figure, O is the centre of the circle. If ∠ABE = 119° and ∠BCD = 116°, find ∠CFD

(i)

70°
(ii)

60°
(iii)

65°
(iv)

85°
(v)

55°

Question 39

39.

In the given figure, O is the centre of the circle . If ∠FIG = 83° and ∠FEH = 63°, find ∠EJF

(i)

29°
(ii)

34°
(iii)

39°
(iv)

44°
(v)

59°

Question 40

40.

In the given triangle S is the circumcentre. If SE = 13.80 cm, find the circumference of the circumcircle

(i)

86.7 cm
(ii)

87.7 cm
(iii)

85.7 cm
(iv)

84.7 cm
(v)

88.7 cm

Question 41

41.

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 42

42.

Two circles with equal radii are

(i)

only similar but not congruent
(ii)

not similar
(iii)

concentric
(iv)

congruent

Question 43

43.

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

(i)

1 cm
(ii)

2 cm
(iii)

5 cm
(iv)

3 cm
(v)

4 cm

Question 44

44.

If two circles of radii 14 cm and 5 cm touch externally, the distance between their centres is

(i)

20 cm
(ii)

19 cm
(iii)

17 cm
(iv)

18 cm
(v)

21 cm

Question 45

45.

In the given figure, O is the centre and FJ is a diameter of the circle and chord FG is equal to chord IJ. If ∠GEI = 44°, find ∠IEJ + ∠GHI

(i)

159°
(ii)

169°
(iii)

164°
(iv)

174°
(v)

189°

Question 46

46.

In the given figure, O is the centre of the circle. If ∠BAC = 57° and ∠ACD = 22°, find ∠CED

(i)

111°
(ii)

131°
(iii)

116°
(iv)

101°
(v)

106°

Question 47

47.

In the given figure, O is the centre of the circle. If ∠FDE = 55°, find reflex ∠EOC

(i)

260°
(ii)

250°
(iii)

265°
(iv)

255°
(v)

280°

Question 48

48.

O is the centre of the circle. If Arc GI = 2 Arc IJ and ∠GOI = 97°, find ∠GJI

(i)

48.5°
(ii)

53.5°
(iii)

58.5°
(iv)

78.5°
(v)

63.5°

Question 49

49.

O is the centre of the circle. If Arc FH = 2 Arc HI and ∠FOH = 98°, find ∠IFH

(i)

29.5°
(ii)

34.5°
(iii)

39.5°
(iv)

54.5°
(v)

24.5°

Question 50

50.

O is the centre of the circle. If Arc AC = 2 Arc CD and ∠AOC = 99°, find ∠ABC

(i)

140.5°
(ii)

135.5°
(iii)

145.5°
(iv)

160.5°
(v)

130.5°

Question 51

51.

In the given figure, a pentagon is inscribed in a circle with centre O. Given IJ = JK = KL and ∠IJK = 130°. Find ∠IHJ

(i)

25°
(ii)

40°
(iii)

35°
(iv)

55°
(v)

30°

Question 52

52.

In the given figure, a pentagon is inscribed in a circle with centre O. Given GH = HI = IJ and ∠GHI = 134°. Find ∠GFJ

(i)

79°
(ii)

74°
(iii)

69°
(iv)

99°
(v)

84°

Question 53

53.

In the given figure, a pentagon is inscribed in a circle with centre O. Given BC = CD = DE and ∠BCD = 130°. Find ∠DOE

(i)

50°
(ii)

60°
(iii)

65°
(iv)

55°
(v)

80°

Question 54

54.

In the given figure, a hexagon is inscribed in a circle with centre O. Given IJ = JK = KL and ∠LMN = 124.75°. Find ∠IMN

(i)

44.75°
(ii)

49.75°
(iii)

64.75°
(iv)

39.75°
(v)

34.75°

Question 55

55.

In the given figure, a hexagon is inscribed in a circle with centre O. Given BC = CD = DE and ∠EFG = 117.57°. Find ∠GBC

(i)

127.43°
(ii)

132.43°
(iii)

152.43°
(iv)

122.43°
(v)

137.43°

Question 56

56.

In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 103° and ∠EAB = 107°. Find ∠ABC

(i)

133°
(ii)

108°
(iii)

118°
(iv)

113°
(v)

103°

Question 57

57.

In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 120° and ∠EAB = 101°. Find ∠CDE

(i)

114°
(ii)

139°
(iii)

109°
(iv)

119°
(v)

124°

Question 58

58.

In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 102° and ∠EAB = 109°. Find ∠AED

(i)

122°
(ii)

147°
(iii)

127°
(iv)

117°
(v)

132°

Assignment Key