EduSahara™ Worksheet

Question 1

1.

In the given figure, O is the centre of the circle. If ∠LJK = 54° and ∠HIL = 97°, find ∠JLK

(i)

59°
(ii)

29°
(iii)

39°
(iv)

44°
(v)

34°

Question 2

2.

In the given figure, IL & JK are two chords of equal length. Given ∠JKO = 48.5°, find ∠IOL

(i)

98°
(ii)

113°
(iii)

93°
(iv)

88°
(v)

83°

Question 3

3.

In the given figure, KLMN is cyclic quadrilateral. If ∠LMN = 94°, find ∠JKN

(i)

109°
(ii)

99°
(iii)

94°
(iv)

124°
(v)

104°

Question 4

4.

In the given figure, GH is a side of regular 5-sided polygon and GI is a side of regular 9-sided polygon inscribed in a circle with centre O. Find ∠GOH

(i)

102°
(ii)

77°
(iii)

87°
(iv)

72°
(v)

82°

Question 5

5.

The perimeter of a circle is called

(i)

chord
(ii)

centre
(iii)

segment
(iv)

circumference
(v)

radius

Question 6

6.

In the given figure, I and J are centres of two circles with equal radii intersecting at K and L. If IJ = 20 cm and KL = 12.8 cm, find the radii of the circles

(i)

13.87 cm
(ii)

11.87 cm
(iii)

10.87 cm
(iv)

9.87 cm
(v)

12.87 cm

Question 7

7.

In the given figure, two circles of radii AC = 10.7 cm & BC = 12.3 cm intersect at C & D. The distance between the centres AB = 20 cm, find the length of CD

(i)

11.32 cm
(ii)

13.32 cm
(iii)

12.32 cm
(iv)

10.32 cm
(v)

9.32 cm

Question 8

8.

△GHI is inscribed in a circle with centre O. If ∠GOH = 134° and ∠HOI = 156°, find ∠IGH

(i)

93°
(ii)

88°
(iii)

78°
(iv)

83°
(v)

108°

Question 9

9.

In the given figure, O is the centre of the circle. HI is a diameter of the circle and JK is equal to radius. Find ∠HLI

(i)

70°
(ii)

90°
(iii)

60°
(iv)

65°
(v)

75°

Question 10

10.

In the given figure, O is the centre of the circle. If ∠ECD = 57.16° and ∠CDE = 73.25°, find the angle ∠CFD

(i)

54.59°
(ii)

49.59°
(iii)

59.59°
(iv)

79.59°
(v)

64.59°

Question 11

11.

In the given figure, O is the centre of the circle. If ∠EFO = 21° and ∠OHE = 38°, find ∠FGH

(i)

126°
(ii)

151°
(iii)

131°
(iv)

121°
(v)

136°

Question 12

12.

If the radius of a circle is 70 cm, what is its circumference?

(i)

442 cm
(ii)

438 cm
(iii)

441 cm
(iv)

439 cm
(v)

440 cm

Question 13

13.

The minor arc of the circle is

(i)

IKJ
(ii)

ILJ
(iii)

IKJMI
(iv)

NIKJN
(v)

NILJN

Question 14

14.

With the vertices of a triangle △IJK as centres, three circles are drawn touching each other externally. If the sides of the triangle are 11 cm , 18 cm and 13 cm , find the radii of the circles

(i)

3 cm , 13 cm & 10 cm respectively
(ii)

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

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

8 cm , 8 cm & 10 cm respectively
(v)

8 cm , 13 cm & 15 cm respectively

Question 15

15.

In the given figure, O is the centre of the circle. If ∠GFH = 54° and ∠FHI = 24°, find ∠HJI

(i)

107°
(ii)

102°
(iii)

112°
(iv)

132°
(v)

117°

Question 16

16.

An arc subtends 43° in its alternate segment. The angle made by its corresponding major arc at the centre is

(i)

284°
(ii)

304°
(iii)

274°
(iv)

279°
(v)

289°

Question 17

17.

If GHIJ is a cyclic parallelogram, then ∠J

(i)

120°
(ii)

90°
(iii)

105°
(iv)

95°
(v)

100°

Question 18

18.

In the given figure, O is the centre of the circle and DF is a diameter. If ∠ECD = 60°, find ∠EDF

(i)

45°
(ii)

60°
(iii)

30°
(iv)

40°
(v)

35°

Question 19

19.

O is the centre of the circle. If ∠GIH = 46° and ∠IGJ = 53°, find x°, y°

(i)

67°, 64°
(ii)

27°, 44°
(iii)

37°, 44°
(iv)

44°, 37°
(v)

47°, 54°

Question 20

20.

In the given figure, O is the centre of the circle and HJ is a diameter. If ∠GOJ = 105° and ∠OJI = 61°, find ∠HIG + ∠IHJ

(i)

96.5°
(ii)

81.5°
(iii)

66.5°
(iv)

71.5°
(v)

76.5°

Question 21

21.

△JKL is inscribed in a circle with centre O. If ∠JOK = 115° and ∠KOL = 135°, find ∠KLJ

(i)

62.5°
(ii)

87.5°
(iii)

67.5°
(iv)

72.5°
(v)

57.5°

Question 22

22.

An arc subtends 56° in its alternate segment. Its corresponding major arc subtends what angle in its (major arc) alternate segment?

(i)

134°
(ii)

124°
(iii)

129°
(iv)

139°
(v)

154°

Question 23

23.

In the given figure, BC , CD , DE and EF are chords and BE , CF are diameters passing through the centre O. If ∠BOC = 68°. Find ∠CDE

(i)

154°
(ii)

129°
(iii)

139°
(iv)

134°
(v)

124°

Question 24

24.

In the given figure, O is the centre of the circle, and OK ⟂ GH. If ∠GHI = 45.5°, find ∠OJI

(i)

49.5°
(ii)

54.5°
(iii)

59.5°
(iv)

74.5°
(v)

44.5°

Question 25

25.

The major sector of the circle is

(i)

HCFDH
(ii)

HCEDH
(iii)

CED
(iv)

CFDGC
(v)

CEDGC

Assignment Key