EduSahara™ Worksheet

Question 1

1.

A chord that passes through the centre of the circle is called

(i)

centre
(ii)

semi-circle
(iii)

segment
(iv)

chord
(v)

diameter

Question 2

2.

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

(i)

diameter
(ii)

circumference
(iii)

semi-circle
(iv)

centre
(v)

segment

Question 3

3.

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

(i)

major segment
(ii)

radius
(iii)

chord
(iv)

circumference
(v)

semi-circle

Question 4

4.

Which of the following statements are true?

a)	A line can meet a circle atmost at two points.
b)	A circle consists of an infinite number of points.
c)	Every circle has a unique centre.
d)	Each radius of a circle is also a chord of the circle.
e)	Every circle has a unique diameter.

(i)

{d,a,b}
(ii)

{d,a}
(iii)

{e,b}
(iv)

{a,b,c}
(v)

{d,e,c}

Question 5

5.

Which of the following statements are true?

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

(i)

{a,b,c}
(ii)

{b,c,e}
(iii)

{a,d,e}
(iv)

{a,b}
(v)

{d,c}

Question 6

6.

In the given triangle S is the circumcentre. If SA = 13.10 cm, find the circumference of the circumcircle

(i)

84.3 cm
(ii)

82.3 cm
(iii)

83.3 cm
(iv)

81.3 cm
(v)

80.3 cm

Question 7

7.

Find the side of the square in the following figure if the radius of the circle is 15.00 cm.

(i)

22.21 cm
(ii)

23.21 cm
(iii)

20.21 cm
(iv)

19.21 cm
(v)

21.21 cm

Question 8

8.

If a chord EF = 22 cm is drawn in a circle with radius OE = 13 cm, find its distance from the centre of the circle

(i)

5.93 cm
(ii)

7.93 cm
(iii)

6.93 cm
(iv)

4.93 cm
(v)

8.93 cm

Question 9

9.

The diameter IJ of a circle with centre 'O' is perpendicular to the chord GH. If GH = 30.00 cm and IK = 7.21 cm, find the radius of the circle.

(i)

20.21 cm
(ii)

18.21 cm
(iii)

17.21 cm
(iv)

19.21 cm
(v)

21.21 cm

Question 10

10.

'D' and 'E' are centres of circles of radii 2 cm and 4 cm such that DE = 10 cm and 'F' is the centre of the circle of radius 'r' cm which touches the above circles externally. If ∠DFE = 90°, find 'r'

(i)

3 cm
(ii)

5 cm
(iii)

2 cm
(iv)

4 cm
(v)

6 cm

Question 11

11.

Which of the following statements are true?

a)	A chord divides a circle into two sectors.
b)	A chord divides a circle into two segments.
c)	The diameter is the longest chord.
d)	Atmost one chord can be drawn on a circle with a certain length.
e)	The radius is the shortest chord.

(i)

{e,a,b}
(ii)

{d,c}
(iii)

{a,b}
(iv)

{b,c}
(v)

{d,c,b}

Question 12

12.

Which of the following statements are true?

a)	No two chords bisects each other.
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)	Equal length chords are equidistant from the centre of the circle.
e)	The farther the chord is from the centre, the larger the angle it subtends at the centre.

(i)

{b,c,d}
(ii)

{e,c}
(iii)

{a,e,d}
(iv)

{a,b}
(v)

{a,b,c}

Question 13

13.

Which of the following statements are true?

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

(i)

{b,a}
(ii)

{a,c,d}
(iii)

{e,c}
(iv)

{b,a,c}
(v)

{b,e,d}

Question 14

14.

Which of the following statements are true?

a)	The longest of all chords of a circle is called diameter.
b)	The midpoint of any diameter of a circle is its centre.
c)	Two chords bisect each other.
d)	The diameter divides the circle into two unequal parts.
e)	A sector is the area enclosed by two radii and a chord.

(i)

{c,a}
(ii)

{d,b,a}
(iii)

{a,b}
(iv)

{d,b}
(v)

{e,c,a}

Question 15

15.

Which of the following statements are true?

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

(i)

{b,c}
(ii)

{d,c}
(iii)

{d,c,b}
(iv)

{e,a,b}
(v)

{a,b}

Question 16

16.

BC , DE , FG , HI are chords of a circle with BC = 7 cm , DE = 3 cm , FG = 7.5 cm and HI = 5.01 cm. The chord farthest from the centre of the circle is

(i)

HI = 5.01 cm
(ii)

FG = 7.5 cm
(iii)

DE = 3 cm
(iv)

BC = 7 cm

Question 17

17.

In the given figure, C and D are centres of two circles with equal radii intersecting at E and F. If CD = 20 cm and EF = 16 cm, find the radii of the circles

(i)

13.81 cm
(ii)

10.81 cm
(iii)

11.81 cm
(iv)

12.81 cm
(v)

14.81 cm

Question 18

18.

In the given figure, two circles of radii GI = 11.5 cm & HI = 14.6 cm intersect at I & J. The distance between the centres GH = 20 cm, find the length of IJ

(i)

17.57 cm
(ii)

18.57 cm
(iii)

14.57 cm
(iv)

15.57 cm
(v)

16.57 cm

Question 19

19.

In the given figure, O is the centre of the circle. L is a point on chord JK such that JL = LK. Find ∠OLJ

(i)

95°
(ii)

90°
(iii)

100°
(iv)

105°
(v)

120°

Question 20

20.

CD is a line segment and F is its mid-point. Three semi-circles are drawn with CF , FD and CD as diameters. E , G and F respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given CE = 6 cm