EduSahara™ Worksheet

Question 1

1.

In the given figure, O is the centre of the circle. If ∠DEH = 113° and ∠EFG = 110°, find ∠FIG

(i)

58°
(ii)

73°
(iii)

43°
(iv)

48°
(v)

53°

Question 2

2.

In the given figure, O is the centre of the circle and CD is a diameter. If ∠DOF = 102°, find ∠CEF

(i)

39°
(ii)

69°
(iii)

49°
(iv)

44°
(v)

54°

Question 3

3.

In the given figure, △FGH is inscribed in a circle. If FG = FH = 17 cm and GH = 20 cm, find the radius of the circle

(i)

9.51 cm
(ii)

8.51 cm
(iii)

12.51 cm
(iv)

11.51 cm
(v)

10.51 cm

Question 4

4.

In the given figure, O is the centre of the circle , chord KL is equal to chord LM and JL is a diameter. If ∠MJL = 44° find ∠KLM

(i)

122°
(ii)

107°
(iii)

97°
(iv)

92°
(v)

102°

Question 5

5.

The opposite angles in a cyclic quadrilateral are

(i)

linear pair
(ii)

complementary
(iii)

equal
(iv)

supplementary

Question 6

6.

If JKLM is a cyclic quadrilateral and ∠J − ∠L = 12°, then ∠L

(i)

94°
(ii)

99°
(iii)

84°
(iv)

114°
(v)

89°

Question 7

7.

In the given figure, △LIJ is a scalene triangle. KI bisects ∠LIJ. Similarly JK bisects ∠IJL. Given ∠JLI = 102°, find ∠JKI

(i)

146°
(ii)

171°
(iii)

141°
(iv)

151°
(v)

156°

Question 8

8.

In the given figure, GHIJ is a cyclic quadrilateral. If ∠GHJ = 63° and ∠HIG = 50°, find ∠HIJ

(i)

113°
(ii)

143°
(iii)

123°
(iv)

118°
(v)

128°

Question 9

9.

In the given figure, O is the centre of the circle and CF is a diameter. If ∠EFB = 90° and ∠BCF = 63°, find ∠CDE

(i)

117°
(ii)

122°
(iii)

132°
(iv)

127°
(v)

147°

Question 10

10.

In the given figure, AD & BC are two chords of equal length. Given ∠DAO = 42.5°, find ∠COB

(i)

105°
(ii)

125°
(iii)

95°
(iv)

100°
(v)

110°

Question 11

11.

Which of the following statements are true?

a)

All diameters of a circle are chords.

b)

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

c)

π
is a rational number.

d)

22
7
is a rational number.

e)

All chords of a circle are diameters.

(i)

{c,a}
(ii)

{a,b,d}
(iii)

{c,e,d}
(iv)

{e,b}
(v)

{c,a,b}

Question 12

12.

In the given figure, △HIJ is an isosceles such that HI = HJ. Given HO = 11 cm, HI = HJ = 17 cm, find IJ

(i)

22.58 cm
(ii)

23.58 cm
(iii)

20.58 cm
(iv)

21.58 cm
(v)

19.58 cm

Question 13

13.

Which of the following statements are true?

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

(i)

{c,e}
(ii)

{d,a,c}
(iii)

{b,e}
(iv)

{b,e,c}
(v)

{a,c}

Question 14

14.

△EFG is inscribed in a circle with centre O. If ∠EOF = 128° and ∠FOG = 164°, find ∠FGE

(i)

79°
(ii)

94°
(iii)

74°
(iv)

69°
(v)

64°

Question 15

15.

In the given figure, DE ∥ FG. Length of chords DE = 20 cm and FG = 24 cm.

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

(i)

14.94 cm
(ii)

12.94 cm
(iii)

16.94 cm
(iv)

15.94 cm
(v)

13.94 cm

Question 16

16.

O is the centre of the circle. If ∠CDB = 44°, find the angle ∠OCB

(i)

76°
(ii)

46°
(iii)

61°
(iv)

51°
(v)

56°

Question 17

17.

In the given figure, ABCD is a cyclic quadrilateral. If ∠ACB = 33° and ∠CDB = 47°, find ∠ABC

(i)

115°
(ii)

110°
(iii)

100°
(iv)

130°
(v)

105°

Question 18

18.

Which of the following statements are true?

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

(i)

{c,a,b}
(ii)

{a,b,e}
(iii)

{c,d,e}
(iv)

{d,b}
(v)

{c,a}

Question 19

19.

Two circles touch internally. G is the centre of the bigger circle and lies on the smaller circle. If ∠DEF = 45°, find ∠D

(i)

60°
(ii)

45°
(iii)

55°
(iv)

75°
(v)

50°

Question 20

20.

In the given figure, a pentagon is inscribed in a circle with centre O. Given CD = DE = EF and ∠CDE = 102°. Find ∠CBD

(i)

39°
(ii)

54°
(iii)

49°
(iv)

69°
(v)

44°

Question 21

21.

In the given figure, O is the centre of the circle. If ∠OFH = 45°, find ∠G

(i)

150°
(ii)

135°
(iii)

140°
(iv)

165°
(v)

145°

Question 22

22.

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)

tangent
(ii)

diameter
(iii)

semi-circle
(iv)

quadrant
(v)

secant

Question 23

23.

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

(i)

27.87 cm
(ii)

24.87 cm
(iii)

28.87 cm
(iv)

25.87 cm
(v)

26.87 cm

Question 24

24.

With the vertices of a triangle △CDE as centres, three circles are drawn touching each other externally. If the sides of the triangle are 10 cm , 16 cm and 14 cm , find the radii of the circles

(i)

4 cm , 6 cm & 15 cm respectively
(ii)

4 cm , 6 cm & 10 cm respectively
(iii)

9 cm , 6 cm & 10 cm respectively
(iv)

4 cm , 11 cm & 10 cm respectively
(v)

9 cm , 11 cm & 15 cm respectively

Question 25

25.

In the given figure, O is the centre of the circle and JL is a diameter. If ∠IKJ = 23° and ∠JIK = 63°, find ∠LJK + ∠IKL

(i)

94°
(ii)

104°
(iii)

124°
(iv)

109°
(v)

99°

Assignment Key