EduSahara™ Worksheet

Question 1

1.

In the given figure, O is the centre of the circle. If ∠HIO = 45° and ∠OKH = 6°, find ∠IJK

(i)

134°
(ii)

139°
(iii)

159°
(iv)

129°
(v)

144°

Question 2

2.

In the given figure, FGHJ is a cyclic quadrilateral where GH and GF are produced to I and E respectively. If ∠EFJ = 83°, find ∠IHJ

(i)

97°
(ii)

112°
(iii)

127°
(iv)

107°
(v)

102°

Question 3

3.

In the given figure, O is the centre of the circle and DF is a diameter. If ∠ECD = 63°, find ∠EDF

(i)

42°
(ii)

37°
(iii)

32°
(iv)

27°
(v)

57°

Question 4

4.

Which of the following statements are true?

a)	A tangent is the limiting case of a secant.
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 secant and a chord are same.

(i)

{e,b,a}
(ii)

{d,c,a}
(iii)

{a,c}
(iv)

{d,c}
(v)

{b,a}

Question 5

5.

In the given figure, O is the centre of the circle. If ∠COD = 73° and ∠DEG = 108°, find ∠FCO

(i)

64.5°
(ii)

69.5°
(iii)

54.5°
(iv)

59.5°
(v)

84.5°

Question 6

6.

(i)

140°
(ii)

135°
(iii)

130°
(iv)

125°
(v)

155°

Question 7

7.

△LMN is inscribed in a circle with centre O. If ∠LOM = 149° and ∠MON = 162°, find ∠NLM

(i)

111°
(ii)

91°
(iii)

86°
(iv)

96°
(v)

81°

Question 8

8.

O is the centre of the circle. If Arc DF = 2 Arc FG and ∠DOF = 93°, find ∠DGF

(i)

76.5°
(ii)

56.5°
(iii)

46.5°
(iv)

61.5°
(v)

51.5°

Question 9

9.

In the given figure, IJ is a side of regular 6-sided polygon and IK is a side of regular 10-sided polygon inscribed in a circle with centre O. Find ∠IOJ

(i)

75°
(ii)

90°
(iii)

60°
(iv)

65°
(v)

70°

Question 10

10.

In the given figure, AD & BC are two chords of equal length. Given ∠DAO = 48.5°, find ∠COB

(i)

88°
(ii)

98°
(iii)

93°
(iv)

83°
(v)

113°

Question 11

11.

In the given figure, F and G are centres of two circles with equal radii intersecting at H and I. If FG = 20 cm and HI = 17.8 cm, find the radii of the circles

(i)

11.39 cm
(ii)

13.39 cm
(iii)

15.39 cm
(iv)

12.39 cm
(v)

14.39 cm

Question 12

12.

In the given figure, HIJKL is a regular pentagon . Find ∠HLJ

(i)

82°
(ii)

72°
(iii)

77°
(iv)

87°
(v)

102°

Question 13

13.

In the given figure, DE , EF , FG and GH are chords and DG , EH are diameters passing through the centre O. If ∠DOE = 77°. Find ∠EFG

(i)

128.5°
(ii)

133.5°
(iii)

158.5°
(iv)

143.5°
(v)

138.5°

Question 14

14.

In the given figure, HIJK is cyclic quadrilateral. If ∠IJK = 88°, find ∠GHK

(i)

93°
(ii)

88°
(iii)

103°
(iv)

98°
(v)

118°

Question 15

15.

Two circles with equal radii are

(i)

not similar
(ii)

concentric
(iii)

congruent
(iv)

only similar but not congruent

Question 16

16.

The point of intersection of the angular bisectors of a triangle is

(i)

circumcentre
(ii)

centroid
(iii)

incentre
(iv)

orthocentre
(v)

excentre

Question 17

17.

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)

{b,d}
(iii)

{a,c,d}
(iv)

{c,d,e}
(v)

{a,b,e}

Question 18

18.

Which of the following statements are true?

a)	If two circles touch internally, their centres and the point of contact form a scalene triangle.
b)	If two circles touch externally, the distance between their centres is the sum of their radii.
c)	If two circles touch externally, the square of the distance between their centres is the sum of the squares of their radii.
d)	If two circles touch internally, the square of the distance between their centres is the difference of the squares of their radii.
e)	If two circles touch internally, the distance between their centres is the difference of their radii.
f)	If two circles touch externally, their centres and the point of contact form an isosceles triangle.

(i)

{b,e}
(ii)

{c,e}
(iii)

{a,e,b}
(iv)

{a,b}
(v)

{d,f,b}

Question 19

19.

If FGHI is a cyclic quadrilateral and ∠F − ∠H = 8°, then ∠H

(i)

86°
(ii)

101°
(iii)

116°
(iv)

91°
(v)

96°

Question 20

20.

Which of the following statements are true?

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