EduSahara™ Worksheet

Question 1

1.

In the given figure, O is the centre of the circle. If ∠LJK = 34° and ∠HIL = 98°, find ∠JLK

(i)

58°
(ii)

48°
(iii)

63°
(iv)

53°
(v)

78°

Question 2

2.

O is the centre of the circle. If ∠HOG = 126° and ∠IOG = 75°, find ∠HGI

(i)

84.5°
(ii)

79.5°
(iii)

109.5°
(iv)

94.5°
(v)

89.5°

Question 3

3.

In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 115° and ∠EAB = 109°. Find ∠CDE

(i)

108.5°
(ii)

118.5°
(iii)

103.5°
(iv)

113.5°
(v)

133.5°

Question 4

4.

In the given figure, JL is a chord which is equal to the radius of the circle. Find ∠M and ∠K

(i)

60° & 120°
(ii)

45° & 135°
(iii)

50° & 130°
(iv)

30° & 150°
(v)

40° & 140°

Question 5

5.

In the given figure, IJ is a side of regular 8-sided polygon and IK is a side of regular 5-sided polygon inscribed in a circle with centre O. Find ∠IKJ

(i)

32.5°
(ii)

22.5°
(iii)

27.5°
(iv)

52.5°
(v)

37.5°

Question 6

6.

Which of the following statements are true?

a)	Angles in the same segment are equal.
b)	Angles in the opposite segments are supplementary.
c)	Angles subtended by equal length arcs in two circles are equal.
d)	Angles in the opposite segments are complementary.

(i)

{c,a}
(ii)

{a,b}
(iii)

{d,b}
(iv)

{c,b,a}
(v)

{c,d,a}

Question 7

7.

In the given figure, JK & LM are diameters of the circle. If ∠JML = 43°, find ∠OLK

(i)

58°
(ii)

53°
(iii)

48°
(iv)

73°
(v)

43°

Question 8

8.

In the given figure, O is the centre of the circle . If ∠DGE = 74° and ∠DCF = 67°, find ∠CHD

(i)

43°
(ii)

58°
(iii)

33°
(iv)

28°
(v)

38°

Question 9

9.

Angle subtended in the major segment is

(i)

zero angle
(ii)

acute angle
(iii)

obtuse angle
(iv)

reflex angle
(v)

straight angle

Question 10

10.

Which of the following statements are true?

a)	Either pair of opposite angles of a cyclic quadrilateral are supplementary.
b)	An isosceles trapezium is cyclic.
c)	A quadrilateral in which the diagonals are equal and bisect each other is cyclic.
d)	The exterior angle of a quadrilateral and its interior opposite angle are supplementary.
e)	All parallelograms are cyclic.

(i)

{d,a}
(ii)

{a,b,c}
(iii)

{e,b}
(iv)

{d,e,c}
(v)

{d,a,b}

Question 11

11.

If CDEF is a cyclic parallelogram, then ∠F

(i)

105°
(ii)

95°
(iii)

120°
(iv)

90°
(v)

100°

Question 12

12.

In the given figure, two circles of radii BD = 12.3 cm & CD = 12.3 cm intersect at D & E. The distance between the centres BC = 20 cm, find the length of DE

(i)

13.32 cm
(ii)

12.32 cm
(iii)

16.32 cm
(iv)

15.32 cm
(v)

14.32 cm

Question 13

13.

In the given figure, O is the centre of the circle. If ∠IGH = 53°, find reflex ∠HOF

(i)

269°
(ii)

254°
(iii)

264°
(iv)

259°
(v)

284°

Question 14

14.

If an arc subtends an angle of x° in its alternate segment, then the angle is subtends at the centre is

(i)

2x°
(ii)

x°

2
(iii)

x°
(iv)

4x°

Question 15

15.

Which of the following statements are true?

a)	A chord divides a circle into two segments.
b)	Atmost one chord can be drawn on a circle with a certain length.
c)	The radius is the shortest chord.
d)	A chord divides a circle into two sectors.
e)	The diameter is the longest chord.

(i)

{b,a}
(ii)

{c,e}
(iii)

{a,e}
(iv)

{d,b,a}
(v)

{c,e,a}

Question 16

16.

In the given figure, O is the centre of the circle. Given ∠BOC = 52°, ∠AED = 80° and ∠COD = 58°, find ∠AOB

(i)

60°
(ii)

55°
(iii)

80°
(iv)

50°
(v)

65°

Question 17

17.

In the given figure, ∠OHG = 18° & ∠OGD = 47°, find ∠FED

(i)

60°
(ii)

80°
(iii)

65°
(iv)

50°
(v)

55°

Question 18

18.

In the given figure, O is the centre of the circle. If ∠ADB = 46° and ∠OAD = 26°, find ∠CBD

(i)

126°
(ii)

131°
(iii)

116°
(iv)

121°
(v)

146°

Question 19

19.

In the given figure, ABCDE is a regular pentagon . Find ∠AEC

(i)

87°
(ii)

72°
(iii)

77°
(iv)

102°
(v)

82°

Question 20

20.

An arc subtends 90° in its alternate segment. The arc is

(i)

minor segment
(ii)

minor arc
(iii)

semi-circle
(iv)

major arc
(v)

major segment

Question 21

21.

Which of the following statements are true?

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

(i)

{a,c}
(ii)

{a,c,d}
(iii)

{a,b,e}
(iv)

{b,d}
(v)

{c,d,e}

Question 22

22.

O is the centre of the circle and OK = JK. Find ∠JOK

(i)

90°
(ii)

70°
(iii)

60°
(iv)

65°
(v)

75°

Question 23

23.

In the given figure, △DAB is a scalene triangle. CA bisects ∠DAB. Similarly BC bisects ∠ABD. Given ∠BDA = 104°, find ∠BCA

(i)

152°
(ii)

157°
(iii)

142°
(iv)

147°
(v)

172°

Question 24

24.

In the given figure, O is the centre of the circle and HJ is a diameter. If ∠IGH = 61°, find ∠IHJ

(i)

39°
(ii)

59°
(iii)

44°
(iv)

29°
(v)

34°

Question 25

25.

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

(i)

incentre
(ii)

circumcentre
(iii)

centroid
(iv)

orthocentre
(v)

excentre

Assignment Key