EduSahara™ Worksheet

Question 1

1.

O is the centre of the circle. If ∠FDG = 32° and ∠DFE = 18°, find ∠EDF

(i)

50°
(ii)

55°
(iii)

40°
(iv)

45°
(v)

70°

Question 2

2.

Which of the following are cyclic quadrilaterals?

a)	rectangle
b)	parallelogram
c)	square
d)	rhombus
e)	triangle
f)	trapezium

(i)

{d,c}
(ii)

{b,a}
(iii)

{e,f,a}
(iv)

{a,c}
(v)

{b,c,a}

Question 3

3.

In the given figure, DE is a side of regular 10-sided polygon and DF is a side of regular 9-sided polygon inscribed in a circle with centre O. Find ∠DEF

(i)

20°
(ii)

50°
(iii)

25°
(iv)

30°
(v)

35°

Question 4

4.

In the given figure, O is the centre of the circle. If ∠GHI = 136°, find ∠OGI

(i)

61°
(ii)

56°
(iii)

76°
(iv)

51°
(v)

46°

Question 5

5.

In the given figure, O is the centre of the circle. If ∠KLI = 78°, find ∠IJK

(i)

102°
(ii)

132°
(iii)

117°
(iv)

112°
(v)

107°

Question 6

6.

In the given figure, O is the centre of the circle , chord BE is equal to chord ED. If ∠BOC = 77° and ∠BED = 109°, find ∠CDE

(i)

89°
(ii)

79°
(iii)

74°
(iv)

84°
(v)

104°

Question 7

7.

Which of the following statements are true?

a)	Exactly two tangents can be drawn parallel to a secant.
b)	Only one circle can be drawn passing through two points.
c)	Only one circle can be drawn with a centre.
d)	Infinite circles can be drawn passing through three collinear points.
e)	Atmost one circle can be drawn passing through three non-collinear points.

(i)

{c,e}
(ii)

{c,e,a}
(iii)

{d,b,a}
(iv)

{b,a}
(v)

{a,e}

Question 8

8.

If DEFG is a cyclic parallelogram, then ∠G

(i)

90°
(ii)

105°
(iii)

100°
(iv)

120°
(v)

95°

Question 9

9.

In the given figure, O is the centre of the circle and chord EF is equal to chord FG and FI is a diameter. If ∠EIF = 27°, find ∠IHG

(i)

127°
(ii)

117°
(iii)

122°
(iv)

147°
(v)

132°

Question 10

10.

In the given figure, O is the centre of the circle , chord DE is equal to chord EF and CE is a diameter. If ∠FCE = 50° find ∠DEF

(i)

95°
(ii)

80°
(iii)

110°
(iv)

85°
(v)

90°

Question 11

11.

In the given figure, a hexagon is inscribed in a circle with centre O. Given IJ = JK = KL and ∠LMN = 127.57°. Find ∠IMN

(i)

42.57°
(ii)

67.57°
(iii)

47.57°
(iv)

37.57°
(v)

52.57°

Question 12

12.

Find the side of the square in the following figure if the radius of the circle is 17.00 cm.

(i)

25.04 cm
(ii)

26.04 cm
(iii)

24.04 cm
(iv)

22.04 cm
(v)

23.04 cm

Question 13

13.

In the given figure, O is the centre of the circle. If ∠IJO = 20° and ∠OLI = 38°, find ∠JKL

(i)

132°
(ii)

137°
(iii)

152°
(iv)

122°
(v)

127°

Question 14

14.

(i)

131°
(ii)

151°
(iii)

121°
(iv)

136°
(v)

126°

Question 15

15.

Angle subtended in the major segment is

(i)

obtuse angle
(ii)

acute angle
(iii)

straight angle
(iv)

right angle
(v)

zero angle

Question 16

16.

In the given figure, a pentagon is inscribed in a circle with centre O. Given HI = IJ = JK and ∠HIJ = 138°. Find ∠HGK

(i)

93°
(ii)

73°
(iii)

68°
(iv)

63°
(v)

78°

Question 17

17.

In the given figure, O is the centre of the circle. Given ∠AED = 84°, ∠COD = 87° and ∠AOB = 38°, find ∠BOC

(i)

53°
(ii)

43°
(iii)

58°
(iv)

73°
(v)

48°

Question 18

18.

If two circles of radii 13 cm and 7 cm touch internally, the distance between their centres is

(i)

8 cm
(ii)

7 cm
(iii)

6 cm
(iv)

5 cm
(v)

4 cm

Question 19

19.

Which of the following statements are true?

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

(i)

{a,b}
(ii)

{c,a}
(iii)

{e,f,a}
(iv)

{c,b,a}
(v)

{d,b}

Question 20

20.

In the given figure, O is the centre of the circle and KM is a diameter. If ∠LJK = 61°, find ∠LKM

(i)

39°
(ii)

44°
(iii)

29°
(iv)

59°
(v)

34°

Question 21

21.

In the given figure, O is the centre of the circle and DG is a diameter. If ∠DGH = 60° and ∠EGF = 32°, find ∠GDF

(i)

28°
(ii)

43°
(iii)

33°
(iv)

58°
(v)

38°

Question 22

22.

In the given figure, O is the centre of the circle. If ∠BEC = 76° and ∠BAD = 62°, find ∠ADC

(i)

47°
(ii)

42°
(iii)

52°
(iv)

72°
(v)

57°

Question 23

23.

Which of the following statements are true?

a)	If a circle can be inscribed in a quadrilateral, it must be a kite.
b)	It is always possible to inscribe a circle in a regular polygon.
c)	It is always possible to inscribe a circle in a quadrilateral.
d)	If a circle can be inscribed in a quadrilateral, the sum of the lengths of a pair of opposite sides is equal to the other pair.
e)	If a circle can be inscribed in a quadrilateral, then it must be a square.

(i)

{a,b}
(ii)

{c,d}
(iii)

{c,d,b}
(iv)

{e,a,b}
(v)

{b,d}

Question 24

24.

O is the centre of the circle. If ∠HJI = 49° and ∠JHK = 33°, find u°, v°

(i)

47°, 41°
(ii)

57°, 41°
(iii)

41°, 57°
(iv)

67°, 51°
(v)

87°, 61°

Question 25

25.

In the given figure, JK is a diameter of the circle with centre O. If ∠KJL = 51.01° and KL = KM, find ∠MLJ

(i)

48.99°
(ii)

38.99°
(iii)

53.99°
(iv)

68.99°
(v)

43.99°

Assignment Key