EduSahara™ Worksheet

Question 1

1.

In the given triangle S is the circumcentre. If SB = 12.80 cm, find the circumference of the circumcircle

(i)

79.5 cm
(ii)

82.5 cm
(iii)

78.5 cm
(iv)

80.5 cm
(v)

81.5 cm

Question 2

2.

Find the side of the square in the following figure if the radius of the circle is 19.00 cm.

(i)

28.87 cm
(ii)

25.87 cm
(iii)

27.87 cm
(iv)

24.87 cm
(v)

26.87 cm

Question 3

3.

If a chord HI = 13 cm is drawn in a circle with radius OH = 9 cm, find its distance from the centre of the circle

(i)

4.22 cm
(ii)

6.22 cm
(iii)

5.22 cm
(iv)

8.22 cm
(v)

7.22 cm

Question 4

4.

The diameter LM of a circle with centre 'O' is perpendicular to the chord JK. If JK = 22.00 cm and LN = 3.60 cm, find the radius of the circle.

(i)

20.60 cm
(ii)

18.60 cm
(iii)

19.60 cm
(iv)

17.60 cm
(v)

16.60 cm

Question 5

5.

With the vertices of a triangle △FGH as centres, three circles are drawn touching each other externally. If the sides of the triangle are 8 cm , 14 cm and 10 cm , find the radii of the circles

(i)

2 cm , 6 cm & 13 cm respectively
(ii)

2 cm , 6 cm & 8 cm respectively
(iii)

7 cm , 6 cm & 8 cm respectively
(iv)

2 cm , 11 cm & 8 cm respectively
(v)

7 cm , 11 cm & 13 cm respectively

Question 6

6.

In the given figure, O is the centre of the circle. I is a point on chord GH such that GI = IH. Find ∠OIG

(i)

90°
(ii)

95°
(iii)

105°
(iv)

120°
(v)

100°

Question 7

7.

Which of the following statements are true?

a)

22
7
is a rational number.

b)

π
is a rational number.

c)

All chords of a circle are diameters.

d)

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

e)

All diameters of a circle are chords.

(i)

{b,c,e}
(ii)

{b,a,d}
(iii)

{c,d}
(iv)

{b,a}
(v)

{a,d,e}

Question 8

8.

JK is a line segment and M is its mid-point. Three semi-circles are drawn with JM , MK and JK as diameters. L , N and M respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given JL = 7 cm

(i)

5.67 cm
(ii)

3.67 cm
(iii)

2.67 cm
(iv)

6.67 cm
(v)

4.67 cm

Question 9

9.

In the given figure, HI ∥ JK. Length of chords HI = 17 cm and JK = 26 cm.

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

(i)

13.44 cm
(ii)

12.44 cm
(iii)

14.44 cm
(iv)

15.44 cm
(v)

11.44 cm

Question 10

10.

In the given figure, AB ∥ CD. Length of chords AB = 15 cm and CD = 17 cm.

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

(i)

12.69 cm
(ii)

13.69 cm
(iii)

10.69 cm
(iv)

11.69 cm
(v)

9.69 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)

8.82 cm
(ii)

11.82 cm
(iii)

9.82 cm
(iv)

10.82 cm
(v)

12.82 cm

Question 12

12.

In the given figure, △CDE is an isosceles such that CD = CE. Given CO = 11 cm, CD = CE = 18 cm, find DE

(i)

20.70 cm
(ii)

22.70 cm
(iii)

21.70 cm
(iv)

19.70 cm
(v)

18.70 cm

Question 13

13.

In the given figure, HK & IJ are two chords of equal length. Given ∠OIJ = 41.5°, find ∠HOK

(i)

107°
(ii)

112°
(iii)

97°
(iv)

127°
(v)

102°

Question 14

14.

In the given figure, △GHI is equilateral. Given GO = 12 cm, find GH

(i)

20.78 cm
(ii)

22.78 cm
(iii)

21.78 cm
(iv)

19.78 cm
(v)

18.78 cm

Question 15

15.

Two concentric circles are of radii 20 cm and 12 cm. Find the length of the chord of the outer circle that touches the inner circle

(i)

34.00 cm
(ii)

32.00 cm
(iii)

30.00 cm
(iv)

31.00 cm
(v)

33.00 cm

Question 16

16.

In the given figure, A and B are centres of two circles with equal radii intersecting at C and D. If AB = 20 cm and CD = 16.4 cm, find the radii of the circles

(i)

14.93 cm
(ii)

12.93 cm
(iii)

10.93 cm
(iv)

13.93 cm
(v)

11.93 cm

Question 17

17.

In the given figure, two circles of radii CE = 14.6 cm & DE = 11.5 cm intersect at E & F. The distance between the centres CD = 20 cm, find the length of EF