EduSahara™ Worksheet

Question 1

1.

In the given triangle S is the circumcentre. If SG = 13.60 cm, find the circumference of the circumcircle

(i)

85.5 cm
(ii)

87.5 cm
(iii)

84.5 cm
(iv)

86.5 cm
(v)

83.5 cm

Question 2

2.

Find the side of the square in the following figure if the radius of the circle is 13.00 cm.

(i)

16.38 cm
(ii)

17.38 cm
(iii)

19.38 cm
(iv)

20.38 cm
(v)

18.38 cm

Question 3

3.

If a chord HI = 13 cm is drawn in a circle with radius OH = 12 cm, find its distance from the centre of the circle

(i)

10.09 cm
(ii)

9.09 cm
(iii)

12.09 cm
(iv)

11.09 cm
(v)

8.09 cm

Question 4

4.

The diameter KL of a circle with centre 'O' is perpendicular to the chord IJ. If IJ = 26.00 cm and KM = 5.69 cm, find the radius of the circle.

(i)

18.69 cm
(ii)

16.69 cm
(iii)

15.69 cm
(iv)

17.69 cm
(v)

19.69 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 , 14 cm and 13 cm , find the radii of the circles

(i)

4 cm , 10 cm & 9 cm respectively
(ii)

9 cm , 10 cm & 14 cm respectively
(iii)

9 cm , 5 cm & 9 cm respectively
(iv)

4 cm , 5 cm & 9 cm respectively
(v)

4 cm , 5 cm & 14 cm respectively

Question 6

6.

In the given figure, O is the centre of the circle. G is a point on chord EF such that EG = GF. Find ∠OGE

(i)

90°
(ii)

105°
(iii)

95°
(iv)

100°
(v)

120°

Question 7

7.

Which of the following statements are true?

a)

All diameters of a circle are chords.

b)

All chords of a circle are diameters.

c)

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

d)

π
is a rational number.

e)

22
7
is a rational number.

(i)

{d,c}
(ii)

{b,d,e}
(iii)

{b,a,c}
(iv)

{a,c,e}
(v)

{b,a}

Question 8

8.

FG is a line segment and I is its mid-point. Three semi-circles are drawn with FI , IG and FG as diameters. H , J and I respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given FH = 8 cm

(i)

4.33 cm
(ii)

3.33 cm
(iii)

6.33 cm
(iv)

5.33 cm
(v)

7.33 cm

Question 9

9.

In the given figure, EF ∥ GH. Length of chords EF = 20 cm and GH = 31 cm.

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

(i)

15.22 cm
(ii)

17.22 cm
(iii)

14.22 cm
(iv)

18.22 cm
(v)

16.22 cm

Question 10

10.

In the given figure, BC ∥ DE. Length of chords BC = 19 cm and DE = 23 cm.

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

(i)

13.57 cm
(ii)

15.57 cm
(iii)

12.57 cm
(iv)

16.57 cm
(v)

14.57 cm

Question 11

11.

In the given figure, △GHI is inscribed in a circle. If GH = GI = 18 cm and HI = 20 cm, find the radius of the circle

(i)

10.82 cm
(ii)

9.82 cm
(iii)

8.82 cm
(iv)

11.82 cm
(v)

12.82 cm

Question 12

12.

In the given figure, △GHI is an isosceles such that GH = GI. Given GO = 11 cm, GH = GI = 18 cm, find HI

(i)

21.70 cm
(ii)

18.70 cm
(iii)

20.70 cm
(iv)

22.70 cm
(v)

19.70 cm

Question 13

13.

In the given figure, HK & IJ are two chords of equal length. Given ∠OIJ = 39°, find ∠HOK

(i)

107°
(ii)

102°
(iii)

132°
(iv)

112°
(v)

117°

Question 14

14.

In the given figure, △BCD is equilateral. Given BO = 12 cm, find BD

(i)

19.78 cm
(ii)

20.78 cm
(iii)

21.78 cm
(iv)

18.78 cm
(v)

22.78 cm

Question 15

15.

Two concentric circles are of radii 17 cm and 10 cm. Find the length of the chord of the outer circle that touches the inner circle

(i)

25.50 cm
(ii)

27.50 cm
(iii)

28.50 cm
(iv)

26.50 cm
(v)

29.50 cm

Question 16

16.

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 = 16.8 cm, find the radii of the circles

(i)

11.06 cm
(ii)

13.06 cm
(iii)

15.06 cm
(iv)

12.06 cm
(v)

14.06 cm

Question 17

17.

In the given figure, two circles of radii DF = 15.9 cm & EF = 9 cm intersect at F & G. The distance between the centres DE = 20 cm, find the length of FG