EduSahara™ Worksheet

Question 1

1.

An arc subtends 57° in its alternate segment. The arc is

(i)

major segment
(ii)

minor arc
(iii)

semi-circle
(iv)

major arc
(v)

quadrant

Question 2

2.

In the given figure, O is the centre of the circle and CF is a diameter. If ∠DEF = 125°, find ∠DBC

(i)

45°
(ii)

40°
(iii)

65°
(iv)

35°
(v)

50°

Question 3

3.

In the given figure, IJKL is cyclic quadrilateral. If ∠JKL = 96°, find ∠HIL

(i)

126°
(ii)

111°
(iii)

101°
(iv)

96°
(v)

106°

Question 4

4.

In the given triangle S is the circumcentre. If SF = 14.20 cm, find the circumference of the circumcircle

(i)

91.3 cm
(ii)

87.3 cm
(iii)

90.3 cm
(iv)

89.3 cm
(v)

88.3 cm

Question 5

5.

In the given figure, a hexagon is inscribed in a circle with centre O. Given IJ = JK = KL and ∠LMN = 126.73°. Find ∠IMN

(i)

36.73°
(ii)

51.73°
(iii)

66.73°
(iv)

41.73°
(v)

46.73°

Question 6

6.

Which of the following statements are true?

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

(i)

{a,b}
(ii)

{c,d,b}
(iii)

{b,d}
(iv)

{c,d}
(v)

{e,a,b}

Question 7

7.

In the given figure, O is the centre of the circle and FH is a diameter. If ∠EOH = 109° and ∠OHG = 62°, find ∠FGE + ∠GFH

(i)

93.5°
(ii)

78.5°
(iii)

63.5°
(iv)

73.5°
(v)

68.5°

Question 8

8.

In the given figure, O is the centre of the circle. If ∠FGJ = 118° and ∠GHI = 118°, find ∠HKI

(i)

56°
(ii)

66°
(iii)

61°
(iv)

71°
(v)

86°

Question 9

9.

In the given figure, O is the centre of the circle and EG is a diameter. If ∠DFE = 23° and ∠EDF = 64°, find ∠GEF + ∠DFG

(i)

108°
(ii)

98°
(iii)

93°
(iv)

103°
(v)

123°

Question 10

10.

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

(i)
D

=

85°

,

E

=

90°

,

F

=

95°

,

G

=

90°
(ii)
D

=

87°

,

E

=

90°

,

F

=

93°

,

G

=

90°
(iii)
D

=

86°

,

E

=

90°

,

F

=

94°

,

G

=

90°
(iv)
D

=

88°

,

E

=

90°

,

F

=

92°

,

G

=

90°
(v)
D

=

89°

,

E

=

90°

,

F

=

91°

,

G

=

90°

Question 11

11.

The diameter EF of a circle with centre 'O' is perpendicular to the chord CD. If CD = 22.00 cm and EG = 3.80 cm, find the radius of the circle.

(i)

16.80 cm
(ii)

18.80 cm
(iii)

15.80 cm
(iv)

19.80 cm
(v)

17.80 cm

Question 12

12.

In the given figure, O is the centre of the circle. If ∠GJH = 74° and ∠GFI = 66°, find ∠FIH

(i)

70°
(ii)

55°
(iii)

40°
(iv)

45°
(v)

50°

Question 13

13.

In the given figure, O is the centre of the circle. If ∠DCE = 51° and ∠CEF = 33°, find ∠EGF

(i)

111°
(ii)

96°
(iii)

126°
(iv)

101°
(v)

106°

Question 14

14.

Find the side of the square in the following figure if the radius of the circle is 11.00 cm.

(i)

16.55 cm
(ii)

14.55 cm
(iii)

17.55 cm
(iv)

15.55 cm
(v)

13.55 cm

Question 15

15.

In the given figure, △MIJ is a scalene triangle. KI & LI trisect ∠MIJ. Similarly JK & JL trisect ∠IJM. Given ∠JMI = 78°, find ∠JLI

(i)

117°
(ii)

122°
(iii)

112°
(iv)

127°
(v)

142°

Question 16

16.

In the given figure, BC is a diameter of the circle with centre O. If ∠CBD = 45.68° and CD = CE, find ∠EDB

(i)

49.32°
(ii)

74.32°
(iii)

59.32°
(iv)

44.32°
(v)

54.32°

Question 17

17.

In the given figure, O is the centre of the circle. If ∠EFI = 88°, find ∠GHI

(i)

118°
(ii)

88°
(iii)

103°
(iv)

98°
(v)

93°

Question 18

18.

JKLMNO is a hexagon inscribed in a circle. Given ∠JKL = 124° & ∠LMN = 126°, find ∠NOJ

(i)

120°
(ii)

125°
(iii)

110°
(iv)

140°
(v)

115°

Question 19

19.

Which of the following statements are true?

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

(i)

{d,a,b}
(ii)

{d,a}
(iii)

{d,e,c}
(iv)

{e,b}
(v)

{a,b,c}

Question 20

20.

Which of the following statements are true?

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

(i)

{b,a,d}
(ii)

{a,d,e}
(iii)

{c,d}
(iv)

{b,a}
(v)

{b,c,e}

Question 21

21.

In the given figure, HIJK is a cyclic quadrilateral. If ∠HJI = 38° and ∠JKI = 36°, find ∠HIJ

(i)

106°
(ii)

111°
(iii)

136°
(iv)

121°
(v)

116°

Question 22

22.

An arc subtends 33° in its alternate segment. The angle made by its corresponding major arc at the centre is

(i)

309°
(ii)

304°
(iii)

299°
(iv)

324°
(v)

294°

Question 23

23.

In the given figure, CD , DE , EF and FG are chords and CF , DG are diameters passing through the centre O. If ∠COD = 75°. Find ∠DEF

(i)

127.5°
(ii)

142.5°
(iii)

132.5°
(iv)

137.5°
(v)

157.5°

Question 24

24.

In the given figure, FG & GC are equal length chords, CE and DF are diameters. Given ∠FGO = 59° find, ∠ODE

(i)

43°
(ii)

28°
(iii)

33°
(iv)

38°
(v)

58°

Question 25

25.

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

(i)

40°
(ii)

55°
(iii)

70°
(iv)

45°
(v)

50°

Assignment Key