EduSahara™ Worksheet

Question 1

1.

In the given figure, O is the centre of the circle. If ∠GEF = 73° and ∠CDG = 77°, find ∠EGF

(i)

40°
(ii)

45°
(iii)

30°
(iv)

35°
(v)

60°

Question 2

2.

In the given figure, H and I are centres of two circles with equal radii intersecting at J and K. If HI = 20 cm and JK = 10.6 cm, find the radii of the circles

(i)

13.32 cm
(ii)

11.32 cm
(iii)

12.32 cm
(iv)

10.32 cm
(v)

9.32 cm

Question 3

3.

An arc subtends 72° in its alternate segment. The arc is

(i)

major segment
(ii)

minor segment
(iii)

quadrant
(iv)

major arc
(v)

minor arc

Question 4

4.

In the given figure, ABCD is a cyclic quadrilateral. If ∠ACB = 39° and ∠CDB = 34°, find ∠ADC

(i)

83°
(ii)

103°
(iii)

73°
(iv)

78°
(v)

88°

Question 5

5.

In the given figure, O is the centre of the circle. If ∠GFH = 45° and ∠FHI = 37°, find ∠HJI

(i)

108°
(ii)

113°
(iii)

103°
(iv)

128°
(v)

98°

Question 6

6.

In the given figure, GH is a side of regular 8-sided polygon and GI is a side of regular 10-sided polygon inscribed in a circle with centre O. Find ∠GHI

(i)

18°
(ii)

28°
(iii)

33°
(iv)

48°
(v)

23°

Question 7

7.

In the given figure, O is the centre of the circle. If ∠FGH = 124°, find ∠HOF + ∠FEH

(i)

309°
(ii)

314°
(iii)

334°
(iv)

319°
(v)

304°

Question 8

8.

O is the centre of the circle and OC = BC. Find reflex ∠COA

(i)

245°
(ii)

240°
(iii)

250°
(iv)

270°
(v)

255°

Question 9

9.

In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 117° and ∠EAB = 103°. Find ∠ABC

(i)

147°
(ii)

122°
(iii)

117°
(iv)

132°
(v)

127°

Question 10

10.

Which of the following are cyclic quadrilaterals?

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

(i)

{d,c}
(ii)

{a,c}
(iii)

{b,a}
(iv)

{e,f,a}
(v)

{b,c,a}

Question 11

11.

O is the centre of the circle. If Arc DF = 2 Arc FG and ∠DOF = 92°, find ∠DGF

(i)

61°
(ii)

46°
(iii)

56°
(iv)

51°
(v)

76°

Question 12

12.

In the given figure, AB & CD are diameters of the circle. If ∠ADC = 59°, find ∠OCB

(i)

59°
(ii)

64°
(iii)

69°
(iv)

74°
(v)

89°

Question 13

13.

In the given figure, a pentagon is inscribed in a circle with centre O. Given FG = GH = HI and ∠FGH = 138°. Find ∠FEG

(i)

21°
(ii)

36°
(iii)

26°
(iv)

31°
(v)

51°

Question 14

14.

O is the centre of the circle. If ∠KML = 39° and ∠MKN = 53°, find v°, w°

(i)

37°, 51°
(ii)

47°, 61°
(iii)

51°, 37°
(iv)

67°, 71°
(v)

27°, 51°

Question 15

15.

In the given figure, ∠ACD = 14° and ∠AED = 20°, find ∠CAD

(i)

66°
(ii)

61°
(iii)

71°
(iv)

86°
(v)

56°

Question 16

16.

Which of the following statements are true?

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

(i)

{d,c}
(ii)

{b,c}
(iii)

{d,c,b}
(iv)

{a,b}
(v)

{e,a,b}

Question 17

17.

Which of the following statements are true?

a)

22
7
is a rational number.

b)

All diameters of a circle are chords.

c)

All chords of a circle are diameters.

d)

π
is a rational number.

e)

A circle divides the plane into three mutually disjoint sets of points.

(i)

{c,a,b}
(ii)

{c,d,e}
(iii)

{a,b,e}
(iv)

{d,b}
(v)

{c,a}

Question 18

18.

In the given figure, O is the centre of the circle. If ∠IOJ = 64° and ∠JKM = 104°, find ∠LIO

(i)

46°
(ii)

61°
(iii)

51°
(iv)

56°
(v)

76°

Question 19

19.

In the given figure, O is the centre of the circle. If ∠DGE = 43.5° and ∠ODG = 38°, find ∠FEG

(i)

143°
(ii)

138°
(iii)

128°
(iv)

158°
(v)

133°

Question 20

20.

The opposite angles in a cyclic quadrilateral are

(i)

equal
(ii)

complementary
(iii)

supplementary
(iv)

linear pair

Question 21

21.

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

(i)
D

=

106°

,

E

=

90°

,

F

=

74°

,

G

=

90°
(ii)
D

=

107°

,

E

=

90°

,

F

=

73°

,

G

=

90°
(iii)
D

=

109°

,

E

=

90°

,

F

=

71°

,

G

=

90°
(iv)
D

=

108°

,

E

=

90°

,

F

=

72°

,

G

=

90°
(v)
D

=

110°

,

E

=

90°

,

F

=

70°

,

G

=

90°

Question 22

22.

In the given figure, JKLM is a cyclic quadrilateral. If ∠JLK = 32° and ∠LMK = 50°, find ∠JKL

(i)

103°
(ii)

98°
(iii)

113°
(iv)

108°
(v)

128°

Question 23

23.

In the given figure, O is the centre of the circle . If ∠DGE = 70° and ∠DCF = 70°, find ∠CHD

(i)

40°
(ii)

60°
(iii)

45°
(iv)

30°
(v)

35°

Question 24

24.

Points which lie on the circumference of the circle are called

(i)

Concurrent points
(ii)

Concyclic points
(iii)

Similar points
(iv)

Coincident points
(v)

Cyclic points

Question 25

25.

Find the missing angle in the following figure?

(i)

64°
(ii)

54°
(iii)

84°
(iv)

59°
(v)

69°

Assignment Key