EduSahara™ Worksheet

Question 1

1.

If the radius of the circumcircle is half the length of a side of the triangle, then the triangle is

(i)

obtuse angled triangle
(ii)

right angle triangle
(iii)

equilateral triangle
(iv)

acute angled triangle

Question 2

2.

In the given figure, O is the centre of the circle. Given ∠DOE = 45°, ∠DHG = 77.5° and ∠FOG = 61°, find ∠EOF

(i)

54°
(ii)

79°
(iii)

59°
(iv)

64°
(v)

49°

Question 3

3.

In the given figure, ∠CEF = 12° and ∠CGF = 25°, find ∠DFC

(i)

83°
(ii)

108°
(iii)

93°
(iv)

88°
(v)

78°

Question 4

4.

In the given figure, find the remaining angles of the quadrilateral.

(i)

I

=

101°

,

J

=

81°
(ii)

I

=

99°

,

J

=

79°
(iii)

I

=

98°

,

J

=

78°
(iv)

I

=

102°

,

J

=

82°
(v)

I

=

100°

,

J

=

80°

Question 5

5.

In the given figure, O is the centre of the circle and HK is a diameter. If ∠JKG = 90° and ∠GHK = 65°, find ∠HIJ

(i)

130°
(ii)

120°
(iii)

145°
(iv)

125°
(v)

115°

Question 6

6.

HIJKLM is a hexagon inscribed in a circle. Given ∠HIJ = 122° & ∠JKL = 130°, find ∠LMH

(i)

118°
(ii)

113°
(iii)

138°
(iv)

108°
(v)

123°

Question 7

7.

In the given figure, O is the centre of the circle and DG is a diameter. If ∠DGH = 61° and ∠EGF = 33°, find ∠GDF

(i)

43°
(ii)

28°
(iii)

58°
(iv)

33°
(v)

38°

Question 8

8.

In the given figure, FGHIJ is a regular pentagon . Find ∠FJH

(i)

72°
(ii)

82°
(iii)

87°
(iv)

77°
(v)

102°

Question 9

9.

In the given figure, DEFG is a cyclic quadrilateral. If ∠DFE = 36° and ∠FGE = 45°, find ∠DGF

(i)

91°
(ii)

111°
(iii)

96°
(iv)

81°
(v)

86°

Question 10

10.

In the given figure, FGHI is a cyclic quadrilateral. If ∠FHG = 34° and ∠HIG = 41°, find ∠FGH

(i)

115°
(ii)

135°
(iii)

120°
(iv)

110°
(v)

105°

Question 11

11.

In the given figure, BCDE is cyclic quadrilateral. If ∠CDE = 87°, find ∠ABE

(i)

102°
(ii)

117°
(iii)

87°
(iv)

97°
(v)

92°

Question 12

12.

GH is the perpendicular bisector of side EF of △DEF. Given ∠DEF = 67° and ∠GDF = 37° , find ∠DFE

(i)

49°
(ii)

69°
(iii)

54°
(iv)

44°
(v)

39°

Question 13

13.

In the given figure, which of the following angle pairs are equal?

(i)

{(i,n),(j,m),(k,p),(l,o)}
(ii)

{(i,m),(l,j),(o,k),(n,p)}
(iii)

{(n,i),(k,o),(p,j),(l,m)}
(iv)

{(i,m),(n,p),(l,k),(j,o)}
(v)

{(l,k),(m,p),(i,o),(n,j)}

Question 14

14.

△EFG is inscribed in a circle with centre O. If ∠EOF = 145° and ∠FOG = 157°, find ∠FGE

(i)

77.5°
(ii)

72.5°
(iii)

82.5°
(iv)

102.5°
(v)

87.5°

Question 15

15.

(i)

160°
(ii)

155°
(iii)

175°
(iv)

145°
(v)

150°

Question 16

16.

In the given figure, O is the centre of the circle. If ∠EFC = 78°, find ∠CDE

(i)

117°
(ii)

107°
(iii)

102°
(iv)

132°
(v)

112°

Question 17

17.

In the given figure, O is the centre of the circle . If ∠ILJ = 75° and ∠IHK = 62°, find ∠HMI

(i)

34°
(ii)

49°
(iii)

19°
(iv)

24°
(v)

29°

Question 18

18.

In the given figure, find the angles of the quadrilateral.

(i)
F

=

83°

,

G

=

90°

,

H

=

97°

,

I

=

90°
(ii)
F

=

87°

,

G

=

90°

,

H

=

93°

,

I

=

90°
(iii)
F

=

86°

,

G

=

90°

,

H

=

94°

,

I

=

90°
(iv)
F

=

84°

,

G

=

90°

,

H

=

96°

,

I

=

90°
(v)
F

=

85°

,

G

=

90°

,

H

=

95°

,

I

=

90°

Question 19

19.

Which of the following statements are true?

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

(i)

{b,e,c}
(ii)

{b,e}
(iii)

{d,a,c}
(iv)

{a,c}
(v)

{c,e}

Question 20

20.

Which of the following statements are true?

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

(i)

{a,b}
(ii)

{a,d,b}
(iii)

{c,d}
(iv)

{b,d}
(v)

{e,f,b}

Question 21

21.

In the given figure, O is the centre of the circle and chord FG is equal to chord GH and GJ is a diameter. If ∠FJG = 28°, find ∠JIH

(i)

118°
(ii)

128°
(iii)

148°
(iv)

133°
(v)

123°

Question 22

22.

In the given figure, O is the centre of the circle. If ∠NLM = 52°, find reflex ∠MOK

(i)

286°
(ii)

266°
(iii)

256°
(iv)

271°
(v)

261°

Question 23

23.

In the given figure, JKLN is a cyclic quadrilateral where KL and KJ are produced to M and I respectively. If ∠IJN = 92°, find ∠MLN

(i)

98°
(ii)

103°
(iii)

93°
(iv)

88°
(v)

118°

Question 24

24.

In the given figure, GE and HD are two lines passing through the points of intersection of the two circles at F and C. If ∠HGF = 97° , find ∠FED

(i)

113°
(ii)

88°
(iii)

83°
(iv)

98°
(v)

93°

Question 25

25.

In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 119° and ∠EAB = 109°. Find ∠AED

(i)

106.5°
(ii)

91.5°
(iii)

101.5°
(iv)

121.5°
(v)

96.5°

Assignment Key