EduSahara™ Worksheet

Question 1

1.

Circles having common centre are called

(i)

congruent circles
(ii)

intersecting circles
(iii)

similar circles
(iv)

concentric circles

Question 2

2.

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

a)	∠DGE = 30°
b)	∠COH = 60°
c)	∠HFE = 90°
d)	∠CED = 60°
e)	∠DOF = 120°

(i)

{d,b}
(ii)

{d,c}
(iii)

{d,e,a}
(iv)

{a,b,c,e}
(v)

{d,a}

Question 3

3.

O is the centre of the circle. If ∠GEH = 39° and ∠EGF = 17°, find ∠FEG

(i)

49°
(ii)

44°
(iii)

34°
(iv)

39°
(v)

64°

Question 4

4.

O is the centre of the circle. If ∠IOJ = 96°, find the angle ∠K

(i)

48°
(ii)

58°
(iii)

53°
(iv)

78°
(v)

63°

Question 5

5.

Which of the following statements are true?

a)	The farther the chord is from the centre, the larger the angle it subtends at the centre.
b)	The longest chord of the circle passes through the centre of the circle.
c)	Equal length chords subtend equal angles at the centre of the circle.
d)	No two chords bisects each other.
e)	Equal length chords are equidistant from the centre of the circle.

(i)

{d,c}
(ii)

{a,b,c}
(iii)

{b,c,e}
(iv)

{a,b}
(v)

{a,d,e}

Question 6

6.

Which of the following statements are true?

a)	Two semi-circles of a circle together make the whole circle.
b)	Every circle has a unique diameter.
c)	An infinite number of chords may be drawn for a circle.
d)	One and only one tangent can be drawn to a circle from a point outside it.
e)	An infinite number of diameters may be drawn for a circle.

(i)

{b,a,c}
(ii)

{b,d,e}
(iii)

{b,a}
(iv)

{d,c}
(v)

{a,c,e}

Question 7

7.

O is the centre of the circle. If Arc AC = 2 Arc CD and ∠AOC = 94°, find ∠ABC

(i)

143°
(ii)

163°
(iii)

133°
(iv)

148°
(v)

138°

Question 8

8.

If the two radii OP and OQ of a circle are at right angles to each other, then the sector OPQ is called a

(i)

quadrant
(ii)

chord
(iii)

secant
(iv)

radius
(v)

major segment

Question 9

9.

Which of the following statements are true?

a)	A tangent is the limiting case of a secant.
b)	A secant and a chord are same.
c)	A secant has two end points.
d)	A radius is a limiting case of a diameter.
e)	A diameter is a limiting case of a chord.

(i)

{c,e}
(ii)

{d,b,a}
(iii)

{a,e}
(iv)

{b,a}
(v)

{c,e,a}

Question 10

10.

In the given figure, GHIK is a cyclic quadrilateral where HI and HG are produced to J and F respectively. If ∠FGK = 82°, find ∠JIK

(i)

128°
(ii)

108°
(iii)

103°
(iv)

98°
(v)

113°

Question 11

11.

Two circles with equal radii are

(i)

only similar but not congruent
(ii)

not similar
(iii)

congruent
(iv)

concentric

Question 12

12.

In the given figure, CD & EF are diameters of the circle. If ∠CDE = 47.5° find, ∠DOE

(i)

90°
(ii)

100°
(iii)

85°
(iv)

115°
(v)

95°

Question 13

13.

In the given figure, O is the centre of the circle. If ∠ABE = 109° and ∠BCD = 108°, find ∠CFD

(i)

52°
(ii)

67°
(iii)

42°
(iv)

37°
(v)

47°

Question 14

14.

GH is a line segment and J is its mid-point. Three semi-circles are drawn with GJ , JH and GH as diameters. I , K and J respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given GI = 6 cm

(i)

2.00 cm
(ii)

4.00 cm
(iii)

3.00 cm
(iv)

5.00 cm
(v)

6.00 cm

Question 15

15.

△FGH is inscribed in a circle with centre O. If ∠FOG = 102° and ∠GOH = 135°, find ∠FGH

(i)

61.5°
(ii)

71.5°
(iii)

66.5°
(iv)

91.5°
(v)

76.5°

Question 16

16.

In the given figure, O is the centre of the circle. If ∠EOF = 98° and ∠FGI = 98°, find ∠HEO

(i)

62°
(ii)

72°
(iii)

57°
(iv)

87°
(v)

67°

Question 17

17.

In the given figure, a pentagon is inscribed in a circle with centre O. Given EF = FG = GH and ∠EFG = 130°. Find ∠GOH

(i)

50°
(ii)

80°
(iii)

65°
(iv)

55°
(v)

60°

Question 18

18.

Which of the following statements are true?

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

(i)

{d,a}
(ii)

{d,a,b}
(iii)

{d,e,c}
(iv)

{e,b}
(v)

{a,b,c}

Question 19

19.

In the given figure BD & CD are equal length chords of the circle. Find ∠DBC

(i)

45°
(ii)

60°
(iii)

50°
(iv)

75°
(v)

55°

Question 20

20.

The diameter JK of a circle with centre 'O' is perpendicular to the chord HI. If HI = 22.00 cm and JL = 4.28 cm, find the radius of the circle.

(i)

15.28 cm
(ii)

18.28 cm
(iii)

17.28 cm
(iv)

16.28 cm
(v)

14.28 cm

Question 21

21.

'O' is the centre of a circle of radius 'r' and 'P' is any point in its plane.
If
OP
> r,then P is

(i)

on the circle
(ii)

inside the circle
(iii)

outside the circle

Question 22

22.

In the given figure, two circles of radii IK = 13.7 cm & JK = 13.7 cm intersect at K & L. The distance between the centres IJ = 20 cm, find the length of KL

(i)

18.73 cm
(ii)

20.73 cm
(iii)

16.73 cm
(iv)

19.73 cm
(v)

17.73 cm

Question 23

23.

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

(i)

D

=

99°

,

E

=

99°
(ii)

D

=

98°

,

E

=

98°
(iii)

D

=

96°

,

E

=

96°
(iv)

D

=

97°

,

E

=

97°
(v)

D

=

95°

,

E

=

95°

Question 24

24.

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

(i)

diameter
(ii)

major segment
(iii)

radius
(iv)

centre
(v)

chord

Question 25

25.

An arc subtends 49° in its alternate segment. The arc is

(i)

minor arc
(ii)

major segment
(iii)

minor segment
(iv)

major arc
(v)

semi-circle

Assignment Key