EduSahara™ Worksheet

Question 1

1.

In the given triangle S is the circumcentre. If SF = 13.20 cm, find the circumference of the circumcircle

(i)

82.0 cm
(ii)

83.0 cm
(iii)

81.0 cm
(iv)

84.0 cm
(v)

85.0 cm

Question 2

2.

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 3

3.

If a chord IJ = 15 cm is drawn in a circle with radius OI = 10 cm, find its distance from the centre of the circle

(i)

7.61 cm
(ii)

4.61 cm
(iii)

5.61 cm
(iv)

8.61 cm
(v)

6.61 cm

Question 4

4.

The diameter HI of a circle with centre 'O' is perpendicular to the chord FG. If FG = 30.00 cm and HJ = 10.81 cm, find the radius of the circle.

(i)

16.81 cm
(ii)

17.81 cm
(iii)

15.81 cm
(iv)

14.81 cm
(v)

13.81 cm

Question 5

5.

With the vertices of a triangle △EFG as centres, three circles are drawn touching each other externally. If the sides of the triangle are 9 cm , 15 cm and 10 cm , find the radii of the circles

(i)

7 cm , 12 cm & 13 cm respectively
(ii)

2 cm , 7 cm & 13 cm respectively
(iii)

2 cm , 12 cm & 8 cm respectively
(iv)

2 cm , 7 cm & 8 cm respectively
(v)

7 cm , 7 cm & 8 cm respectively

Question 6

6.

In the given figure, O is the centre of the circle. J is a point on chord HI such that HJ = JI. Find ∠OJH

(i)

120°
(ii)

100°
(iii)

90°
(iv)

105°
(v)

95°

Question 7

7.

Which of the following statements are true?

a)

All chords of a circle are diameters.

b)

π
is a rational number.

c)

All diameters of a circle are chords.

d)

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

e)

22
7
is a rational number.

(i)

{a,c}
(ii)

{a,b,e}
(iii)

{c,d,e}
(iv)

{a,c,d}
(v)

{b,d}

Question 8

8.

EF is a line segment and H is its mid-point. Three semi-circles are drawn with EH , HF and EF as diameters. G , I and H respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given EG = 8 cm

(i)

7.33 cm
(ii)

3.33 cm
(iii)

6.33 cm
(iv)

4.33 cm
(v)

5.33 cm

Question 9

9.

In the given figure, GH ∥ IJ. Length of chords GH = 20 cm and IJ = 30 cm.

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

(i)

16.95 cm
(ii)

15.95 cm
(iii)

17.95 cm
(iv)

13.95 cm
(v)

14.95 cm

Question 10

10.

In the given figure, FG ∥ HI. Length of chords FG = 21 cm and HI = 21 cm.

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

(i)

11.83 cm
(ii)

14.83 cm
(iii)

15.83 cm
(iv)

12.83 cm
(v)

13.83 cm

Question 11

11.

In the given figure, △CDE is inscribed in a circle. If CD = CE = 19 cm and DE = 20 cm, find the radius of the circle

(i)

9.17 cm
(ii)

13.17 cm
(iii)

10.17 cm
(iv)

11.17 cm
(v)

12.17 cm

Question 12

12.

In the given figure, △EFG is an isosceles such that EF = EG. Given EO = 13 cm, EF = EG = 22 cm, find FG

(i)

25.45 cm
(ii)

22.45 cm
(iii)

21.45 cm
(iv)

23.45 cm
(v)

24.45 cm

Question 13

13.

In the given figure, IL & JK are two chords of equal length. Given ∠OLI = 43.5°, find ∠KOJ

(i)

93°
(ii)

103°
(iii)

98°
(iv)

108°
(v)

123°

Question 14

14.

In the given figure, △IJK is equilateral. Given IO = 12 cm, find IJ

(i)

20.78 cm
(ii)

18.78 cm
(iii)

19.78 cm
(iv)

21.78 cm
(v)

22.78 cm

Question 15

15.

Two concentric circles are of radii 18 cm and 12 cm. Find the length of the chord of the outer circle that touches the inner circle

(i)

26.83 cm
(ii)

24.83 cm
(iii)

25.83 cm
(iv)

27.83 cm
(v)

28.83 cm

Question 16

16.

In the given figure, B and C are centres of two circles with equal radii intersecting at D and E. If BC = 20 cm and DE = 19.6 cm, find the radii of the circles

(i)

13.00 cm
(ii)

15.00 cm
(iii)

12.00 cm
(iv)

16.00 cm
(v)

14.00 cm

Question 17

17.

In the given figure, two circles of radii EG = 12.6 cm & FG = 12.6 cm intersect at G & H. The distance between the centres EF = 20 cm, find the length of GH