EduSahara™ Worksheet

Question 1

1.

The segment of the circle containing the centre of the circle is called

(i)

diameter
(ii)

radius
(iii)

major segment
(iv)

semi-circle
(v)

segment

Question 2

2.

In the given figure, FGHIJK is a regular hexagon inscribed in a circle with centre O. Which of the following are true?

a)	∠GOI = 120°
b)	∠KIH = 90°
c)	∠FHG = 60°
d)	∠GJH = 30°
e)	∠FOK = 60°

(i)

{c,a}
(ii)

{c,d}
(iii)

{a,b,d,e}
(iv)

{c,b}
(v)

{c,e,a}

Question 3

3.

△ABC is inscribed in a circle with centre O. If ∠AOB = 104° and ∠BOC = 123°, find ∠BCA

(i)

67°
(ii)

62°
(iii)

57°
(iv)

52°
(v)

82°

Question 4

4.

If the radius of a circle is 91 cm, what is its circumference?

(i)

570 cm
(ii)

571 cm
(iii)

572 cm
(iv)

573 cm
(v)

574 cm

Question 5

5.

An arc subtends 63° in its alternate segment. Its corresponding major arc subtends what angle in its (major arc) alternate segment?

(i)

122°
(ii)

117°
(iii)

147°
(iv)

132°
(v)

127°

Question 6

6.

In the given figure, GE and HD are two lines passing through the points of intersection of the two circles at F and C. If ∠HGF = 99° , find ∠FED

(i)

91°
(ii)

96°
(iii)

81°
(iv)

111°
(v)

86°

Question 7

7.

A line segment joining any point on the circle with its centre is called

(i)

diameter
(ii)

chord
(iii)

segment
(iv)

radius
(v)

semi-circle

Question 8

8.

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

(i)

centroid
(ii)

incentre
(iii)

orthocentre
(iv)

circumcentre
(v)

excentre

Question 9

9.

Circles having common centre are called

(i)

concentric circles
(ii)

similar circles
(iii)

intersecting circles
(iv)

congruent circles

Question 10

10.

In the given figure, O is the centre of the circle. If ∠JIK = 57° and ∠IKL = 22°, find ∠KML

(i)

111°
(ii)

101°
(iii)

131°
(iv)

116°
(v)

106°

Question 11

11.

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 in the opposite segments are complementary.
d)	Angles subtended by equal length arcs in two circles are equal.

(i)

{c,d,a}
(ii)

{c,a}
(iii)

{a,b}
(iv)

{d,b}
(v)

{c,b,a}

Question 12

12.

An arc subtends 51° in its alternate segment. The arc is

(i)

minor arc
(ii)

major arc
(iii)

quadrant
(iv)

major segment
(v)

minor segment

Question 13

13.

In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 105° and ∠EAB = 119°. Find ∠AED

(i)

117.5°
(ii)

122.5°
(iii)

142.5°
(iv)

127.5°
(v)

112.5°

Question 14

14.

A chord of a circle divides the whole circular region into two parts, each called a

(i)

centre
(ii)

chord
(iii)

radius
(iv)

circumference
(v)

segment

Question 15

15.

O is the centre of the circle and ∠KHJ = 35°, find ∠HIJ

(i)

135°
(ii)

125°
(iii)

140°
(iv)

130°
(v)

155°

Question 16

16.

In the given figure, GH & IJ are diameters of the circle. If ∠GHI = 60.5° find, ∠HOI

(i)

74°
(ii)

89°
(iii)

59°
(iv)

69°
(v)

64°

Question 17

17.

In the given figure, O is the centre of the circle. If ∠GHI = 124°, find ∠IOG + ∠GFI

(i)

304°
(ii)

334°
(iii)

314°
(iv)

309°
(v)

319°

Question 18

18.

Which of the following statements are true?

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

(i)

{a,b,c}
(ii)

{a,b}
(iii)

{d,c}
(iv)

{b,c,e}
(v)

{a,d,e}

Question 19

19.

In the given figure, O is the centre of the circle and KN is a diameter. If ∠LMN = 128°, find ∠LJK

(i)

68°
(ii)

53°
(iii)

43°
(iv)

48°
(v)

38°

Question 20

20.

In the given figure, CD ∥ EF. Length of chords CD = 14 cm and EF = 20 cm.

If the distance between the chords is
4 cm
,
find the radius of the circle

(i)

12.92 cm
(ii)

11.92 cm
(iii)

9.92 cm
(iv)

10.92 cm
(v)

8.92 cm

Question 21

21.

Find the points belonging to the circle

(i)

{H,K}
(ii)

{J,M}
(iii)

{K,I}
(iv)

{H,J}
(v)

{I,L}

Question 22

22.

The mid-point of the diameter of a circle is called

(i)

circumference
(ii)

major segment
(iii)

centre
(iv)

chord
(v)

semi-circle

Question 23

23.

Two circles are of radii 3 cm and 1 cm. If the distance between their centres is 8 cm, what is the length of their transverse common tangent?

(i)

5.93 cm
(ii)

4.93 cm
(iii)

6.93 cm
(iv)

7.93 cm
(v)

8.93 cm

Question 24

24.

△DEF is inscribed in a circle with centre O. If ∠DOE = 129° and ∠EOF = 153°, find ∠FDE

(i)

106.5°
(ii)

81.5°
(iii)

91.5°
(iv)

76.5°
(v)

86.5°

Question 25

25.

'H' and 'I' are centres of circles of radii 2 cm and 9 cm such that HI = 17 cm and 'J' is the centre of the circle of radius 'r' cm which touches the above circles externally. If ∠HJI = 90°, find 'r'

(i)

8 cm
(ii)

5 cm
(iii)

7 cm
(iv)

6 cm
(v)

4 cm

Assignment Key