EduSahara™ Worksheet

Question 1

1.

In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 107° and ∠EAB = 102°. Find ∠EAD

(i)

29°
(ii)

59°
(iii)

34°
(iv)

39°
(v)

44°

Question 2

2.

In the given figure, IJ is a side of regular 9-sided polygon and IK is a side of regular 8-sided polygon inscribed in a circle with centre O. Find ∠IOJ

(i)

45°
(ii)

40°
(iii)

55°
(iv)

70°
(v)

50°

Question 3

3.

In the given figure, AB is a side of regular 10-sided polygon and AC is a side of regular 9-sided polygon inscribed in a circle with centre O. Find ∠ACB

(i)

18°
(ii)

48°
(iii)

33°
(iv)

28°
(v)

23°

Question 4

4.

In the given figure, GH is a side of regular 5-sided polygon and GI is a side of regular 10-sided polygon inscribed in a circle with centre O. Find ∠GHI

(i)

48°
(ii)

33°
(iii)

18°
(iv)

28°
(v)

23°

Question 5

5.

In the given figure, O is the centre of the circle. EF is a diameter of the circle and GH is equal to radius. Find ∠EIF

(i)

70°
(ii)

90°
(iii)

60°
(iv)

65°
(v)

75°

Question 6

6.

In the given figure, O is the centre of the circle. If ∠ILJ = 84° and ∠IHK = 63°, find ∠HKJ

(i)

33°
(ii)

43°
(iii)

38°
(iv)

48°
(v)

63°

Question 7

7.

In the given figure, O is the centre of the circle, and OL ⟂ HI. If ∠HIJ = 41.5°, find ∠HOJ

(i)

88°
(ii)

93°
(iii)

113°
(iv)

98°
(v)

83°

Question 8

8.

In the given figure, O is the centre of the circle, and OJ ⟂ FG. If ∠FGH = 37.5°, find ∠OIH

(i)

67.5°
(ii)

82.5°
(iii)

52.5°
(iv)

62.5°
(v)

57.5°

Question 9

9.

In the given figure, O is the centre of the circle. If ∠IGH = 70.72° and ∠GHI = 74.9°, find the angle ∠GJH

(i)

49.38°
(ii)

39.38°
(iii)

44.38°
(iv)

64.38°
(v)

34.38°

Question 10

10.

Which of the following statements are true?

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

(i)

{c,a,d}
(ii)

{b,e,d}
(iii)

{b,e}
(iv)

{a,d}
(v)

{d,e}

Question 11

11.

Which of the following statements are true?

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

(i)

{b,a,c}
(ii)

{a,c,e}
(iii)

{d,c}
(iv)

{b,a}
(v)

{b,d,e}

Question 12

12.

Which of the following statements are true?

a)	A sector is the area enclosed by two radii and a chord.
b)	The diameter divides the circle into two unequal parts.
c)	The area enclosed by a chord and its major arc is called major segment.
d)	A circle divides the plane on which it lies into three parts.
e)	The area enclosed by a chord and its minor arc is called minor segment.

(i)

{a,c}
(ii)

{a,b,e}
(iii)

{a,c,d}
(iv)

{c,d,e}
(v)

{b,d}

Question 13

13.

Which of the following statements are true?

a)	A sector is the area enclosed by two radii and a chord.
b)	The diameter divides the circle into two unequal parts.
c)	The midpoint of any diameter of a circle is its centre.
d)	The longest of all chords of a circle is called diameter.
e)	Two chords bisect each other.

(i)

{c,d}
(ii)

{b,d}
(iii)

{e,a,c}
(iv)

{a,c}
(v)

{b,d,c}

Question 14

14.

Which of the following statements are true?

a)	If a rhombus is cyclic, it is a square.
b)	If a trapezium is cyclic, it is a rectangle.
c)	If a parallelogram is cyclic, it is a rectangle.
d)	A cyclic quadrilateral is a regular polygon.
e)	If a kite is cyclic, it is a square.

(i)

{b,a}
(ii)

{a,c}
(iii)

{e,b,a}
(iv)

{d,c}
(v)

{d,c,a}

Question 15

15.

Which of the following statements are true?

a)	Only one circle can be drawn with a centre.
b)	Infinite circles can be drawn passing through three collinear points.
c)	Atmost one circle can be drawn passing through three non-collinear points.
d)	Only one circle can be drawn passing through two points.
e)	Exactly two tangents can be drawn parallel to a secant.

(i)

{a,c}
(ii)

{b,e,c}
(iii)

{b,e}
(iv)

{d,a,c}
(v)

{c,e}

Question 16

16.

Which of the following are cyclic quadrilaterals?

a)	parallelogram
b)	rectangle
c)	rhombus
d)	trapezium
e)	triangle
f)	square

(i)

{d,e,b}
(ii)

{a,b}
(iii)

{b,f}
(iv)

{c,f}
(v)

{a,f,b}

Question 17

17.

Which of the following statements are true?

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

(i)

{c,e,a}
(ii)

{a,e}
(iii)

{b,a}
(iv)

{d,b,a}
(v)

{c,e}

Question 18

18.

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

(i)

{b,e}
(ii)

{a,e,c}
(iii)

{d,f,c}
(iv)

{c,e}
(v)

{a,c}

Question 19

19.

Which of the following statements are true?

a)	It is always possible to inscribe a circle in a regular polygon.
b)	It is always possible to inscribe a circle in a quadrilateral.
c)	If a circle can be inscribed in a quadrilateral, it must be a kite.
d)	If a circle can be inscribed in a quadrilateral, then it must be a square.
e)	If a circle can be inscribed in a quadrilateral, the sum of the lengths of a pair of opposite sides is equal to the other pair.

(i)

{a,e}
(ii)

{b,a}
(iii)

{c,e}
(iv)

{d,b,a}
(v)

{c,e,a}

Question 20

20.

Which of the following statements are true?

a)	Angles in the opposite segments are supplementary.
b)	Angles in the same segment are equal.
c)	Angles subtended by equal length arcs in two circles are equal.
d)	Angles in the opposite segments are complementary.

(i)

{c,a}
(ii)

{d,b}
(iii)

{a,b}
(iv)

{c,b,a}
(v)

{c,d,a}

Question 21

21.

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

(i)

incentre
(ii)

centroid
(iii)

orthocentre
(iv)

circumcentre
(v)

excentre

Question 22

22.

If an arc subtends an angle of x° in its alternate segment, then the angle is subtends at the centre is

(i)

2x°
(ii)

x°

2
(iii)

x°
(iv)

4x°

Question 23

23.

An arc subtends 90° in its alternate segment. The arc is

(i)

semi-circle
(ii)

minor segment
(iii)

major arc
(iv)

major segment
(v)

minor arc

Question 24

24.

An arc subtends 163° in its alternate segment. The arc is

(i)

major arc
(ii)

semi-circle
(iii)

quadrant
(iv)

minor arc
(v)

major segment

Question 25

25.

An arc subtends 51° in its alternate segment. The arc is

(i)

quadrant
(ii)

major arc
(iii)

minor arc
(iv)

major segment
(v)

minor segment

Question 26

26.

An arc subtends 65° in its alternate segment. Its corresponding major arc subtends what angle in its (major arc) alternate segment?

(i)

115°
(ii)

130°
(iii)

120°
(iv)

145°
(v)

125°

Question 27

27.

An arc subtends 48° in its alternate segment. The angle made by its corresponding major arc at the centre is

(i)

279°
(ii)

264°
(iii)

269°
(iv)

294°
(v)

274°

Question 28

28.

In the given figure, two circles of radii AC = 9.4 cm & BC = 13.7 cm intersect at C & D. The distance between the centres AB = 20 cm, find the length of CD

(i)

11.29 cm
(ii)

13.29 cm
(iii)

9.29 cm
(iv)

12.29 cm
(v)

10.29 cm

Question 29

29.

The angle subtended by the semicircle at the centre is

(i)

190°
(ii)

210°
(iii)

185°
(iv)

180°
(v)

195°

Question 30

30.

The angle subtended by the diameter at any point on the circle is

(i)

90°
(ii)

95°
(iii)

105°
(iv)

120°
(v)

100°

Question 31

31.

Angle subtended by the major arc at the centre is

(i)

reflex angle
(ii)

zero angle
(iii)

complete angle
(iv)

acute angle
(v)

right angle

Question 32

32.

Angle subtended in the major segment is

(i)

right angle
(ii)

acute angle
(iii)

straight angle
(iv)

obtuse angle
(v)

complete angle

Question 33

33.

The opposite angles in a cyclic quadrilateral are

(i)

linear pair
(ii)

equal
(iii)

complementary
(iv)

supplementary

Question 34

34.

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

(i)

right angle triangle
(ii)

obtuse angled triangle
(iii)

acute angled triangle
(iv)

equilateral triangle

Question 35

35.

Circles having common centre are called

(i)

concentric circles
(ii)

congruent circles
(iii)

intersecting circles
(iv)

similar circles

Question 36

36.

If two circles are concentric, then

(i)

their radii are same
(ii)

their centres are same
(iii)

their diameters are same
(iv)

their perimeters are same

Question 37

37.

In the given figure, IJKL is cyclic quadrilateral. If ∠JKL = 78°, find ∠HIL

(i)

78°
(ii)

83°
(iii)

108°
(iv)

93°
(v)

88°

Question 38

38.

In the given figure, HI & JK are diameters of the circle. If ∠HIJ = 44° find, ∠IOJ

(i)

122°
(ii)

92°
(iii)

107°
(iv)

102°
(v)

97°

Question 39

39.

In the given figure, BC & DE are diameters of the circle. If ∠BED = 56°, find ∠ODC

(i)

66°
(ii)

61°
(iii)

71°
(iv)

56°
(v)

86°

Question 40

40.

In the given figure CE & DE are equal length chords of the circle. Find ∠ECD

(i)

50°
(ii)

45°
(iii)

60°
(iv)

75°
(v)

55°

Question 41

41.

In the given figure, AB is a diameter of the circle with centre O. If ∠BAC = 21.94° and BC = BD, find ∠DCA

(i)

98.06°
(ii)

73.06°
(iii)

78.06°
(iv)

83.06°
(v)

68.06°

Question 42

42.

In the given figure, O is the centre of the circle. If ∠OGI = 38°, find ∠H

(i)

138°
(ii)

158°
(iii)

133°
(iv)

128°
(v)

143°

Question 43

43.

In the given figure, O is the centre of the circle. If ∠JKL = 127°, find ∠OJL

(i)

67°
(ii)

42°
(iii)

37°
(iv)

52°
(v)

47°

Question 44

44.

In the given figure, O is the centre of the circle. If ∠EFO = 45° and ∠OHE = 6°, find ∠FGH

(i)

139°
(ii)

134°
(iii)

159°
(iv)

129°
(v)

144°

Question 45

45.

In the given figure, O is the centre of the circle. If ∠CDO = 27° and ∠OFC = 31°, find ∠DOF

(i)

131°
(ii)

146°
(iii)

126°
(iv)

121°
(v)

116°

Question 46

46.

In the given figure, IJKL is a cyclic quadrilateral. If ∠IKJ = 38° and ∠KLJ = 39°, find ∠IJK

(i)

108°
(ii)

113°
(iii)

133°
(iv)

103°
(v)

118°

Question 47

47.

In the given figure, GHIJ is a cyclic quadrilateral. If ∠GIH = 32° and ∠IJH = 40°, find ∠GJI

(i)

102°
(ii)

87°
(iii)

77°
(iv)

82°
(v)

72°

Question 48

48.

In the given figure, FGHIJK is a regular hexagon. Find ∠FHG

(i)

35°
(ii)

30°
(iii)

40°
(iv)

45°
(v)

60°

Question 49

49.

In the given figure, ABCDEF is a regular hexagon. Find ∠ADC

(i)

90°
(ii)

75°
(iii)

60°
(iv)

70°
(v)

65°

Question 50

50.

With the vertices of a triangle △DEF as centres, three circles are drawn touching each other externally. If the sides of the triangle are 9 cm , 13 cm and 12 cm , find the radii of the circles

(i)

4 cm , 10 cm & 8 cm respectively
(ii)

4 cm , 5 cm & 8 cm respectively
(iii)

4 cm , 5 cm & 13 cm respectively
(iv)

9 cm , 5 cm & 8 cm respectively
(v)

9 cm , 10 cm & 13 cm respectively

Question 51

51.

O is the centre of the circle. If ∠EFD = 50.5°, find the angle ∠OED

(i)

69.5°
(ii)

44.5°
(iii)

49.5°
(iv)

54.5°
(v)

39.5°

Question 52

52.

In the given figure, ABCD is a cyclic quadrilateral. If ∠ABD = 74° and ∠BCA = 44°, find ∠DAB

(i)

77°
(ii)

72°
(iii)

92°
(iv)

62°
(v)

67°

Question 53

53.

DE is the perpendicular bisector of side BC of △ABC. Given ∠ABC = 68° and ∠DAC = 40° , find ∠ACB

(i)

47°
(ii)

37°
(iii)

32°
(iv)

42°
(v)

62°

Question 54

54.

In the given figure, △EBC is a scalene triangle. DB bisects ∠EBC. Similarly CD bisects ∠BCE. Given ∠CEB = 104°, find ∠CDB

(i)

142°
(ii)

152°
(iii)

157°
(iv)

147°
(v)

172°

Question 55

55.

In the given figure, △JFG is a scalene triangle. HF & IF trisect ∠JFG. Similarly GH & GI trisect ∠FGJ. Given ∠GJF = 60°, find ∠GHF

(i)

145°
(ii)

170°
(iii)

155°
(iv)

150°
(v)

140°

Question 56

56.

In the given figure, △JFG is a scalene triangle. HF & IF trisect ∠JFG. Similarly GH & GI trisect ∠FGJ. Given ∠GJF = 96°, find ∠GIF

(i)

129°
(ii)

154°
(iii)

139°
(iv)

134°
(v)

124°

Question 57

57.

In the given figure, ∠DFG = 15° and ∠DHG = 30°, find ∠FDG

(i)

60°
(ii)

45°
(iii)

55°
(iv)

75°
(v)

50°

Question 58

58.

In the given figure, ∠EGH = 12° and ∠EIH = 32°, find ∠FHE

(i)

83°
(ii)

108°
(iii)

88°
(iv)

93°
(v)

78°

Question 59

59.

In the given figure, AB , BC , CD and DE are chords and AD , BE are diameters passing through the centre O. If ∠AOB = 57°. Find ∠BCD

(i)

118.5°
(ii)

123.5°
(iii)

133.5°
(iv)

148.5°
(v)

128.5°

Question 60

60.

In the given figure, IJKLMN is a regular hexagon inscribed in a circle with centre O. Which of the following are true?

a)	∠IKJ = 60°
b)	∠JOL = 120°
c)	∠ION = 60°
d)	∠NLK = 90°
e)	∠JMK = 30°

(i)

{a,b}
(ii)

{a,d}
(iii)

{a,c}
(iv)

{a,e,b}
(v)

{b,c,d,e}

Question 61

61.

In the given figure, ABCDE is a regular pentagon . Find ∠AEC

(i)

77°
(ii)

87°
(iii)

82°
(iv)

72°
(v)

102°

Question 62

62.

In the given figure, IK is a chord which is equal to the radius of the circle. Find ∠L and ∠J

(i)

45° & 135°
(ii)

60° & 120°
(iii)

50° & 130°
(iv)

30° & 150°
(v)

40° & 140°

Question 63

63.

In the given figure, FGHJ is a cyclic quadrilateral where GH and GF are produced to I and E respectively. If ∠EFJ = 101°, find ∠IHJ

(i)

109°
(ii)

89°
(iii)

84°
(iv)

79°
(v)

94°

Question 64

64.

In the given figure, ∠E = 54° , ∠H = 56° and ∠I = 121°, find ∠HFG

(i)

51°
(ii)

61°
(iii)

66°
(iv)

56°
(v)

81°

Question 65

65.

Which of the following statements are true?

a)	A cyclic kite is a square.
b)	A cyclic trapezium is a rectangle.
c)	A cyclic rhombus is a square.
d)	A cyclic parallelogram is a rectangle.
e)	A cyclic parallelogram is a rhombus.

(i)

{a,c}
(ii)

{b,d}
(iii)

{b,d,c}
(iv)

{c,d}
(v)

{e,a,c}

Question 66

66.

Which of the following statements are true?

a)	All parallelograms are cyclic.
b)	An isosceles trapezium is cyclic.
c)	The exterior angle of a quadrilateral and its interior opposite angle are supplementary.
d)	A quadrilateral in which the diagonals are equal and bisect each other is cyclic.
e)	Either pair of opposite angles of a cyclic quadrilateral are supplementary.

(i)

{a,b}
(ii)

{a,c,e}
(iii)

{b,d,e}
(iv)

{c,d}
(v)

{a,b,d}

Question 67

67.

Which of the following are not cyclic quadrilaterals?

a)	isosceles trapezium
b)	rectangle
c)	square
d)	kite
e)	rhombus

(i)

{b,e,d}
(ii)

{d,e}
(iii)

{b,e}
(iv)

{a,d}
(v)

{c,a,d}

Question 68

68.

Which of the following statements are true?

a)	Angle subtended in the major segment is obtuse.
b)	The angle subtended in a semicircle is a right angle.
c)	If two chords are equal, then they are equidistant from the centre of the circle.
d)	Angle subtended by the major arc at the centre is acute.
e)	Angle subtended by the major arc in its alternate segment is obtuse.

(i)

{a,b,c}
(ii)

{a,d,e}
(iii)

{b,c,e}
(iv)

{d,c}
(v)

{a,b}

Question 69

69.

In triangle GHI, if a circle is drawn with HI as diameter and if it passes through G it is a

(i)

acute angled triangle
(ii)

equilateral triangle
(iii)

right angle triangle
(iv)

obtuse angled triangle

Question 70

70.

Which of the following statements are true?

a)

π
is a rational number.

b)

All chords of a circle are diameters.

c)

22
7
is a rational number.

d)

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

e)

All diameters of a circle are chords.

(i)

{b,d}
(ii)

{a,c}
(iii)

{c,d,e}
(iv)

{a,c,d}
(v)

{a,b,e}

Question 71

71.

In the given figure, which of the following are true?

a)	∠B + ∠OCD + ∠ODC = 2 ∠B
b)	∠B + ∠ODC = 90°
c)	∠B + ∠OCD = 90°
d)	∠B + ∠COD = 180°
e)	∠B + ∠OCD = 120°

(i)

{a,b}
(ii)

{b,c}
(iii)

{d,c}
(iv)

{e,a,b}
(v)

{d,c,b}

Question 72

72.

If BCDE is a cyclic quadrilateral and ∠B − ∠D = 30°, then ∠D

(i)

105°
(ii)

80°
(iii)

75°
(iv)

85°
(v)

90°

Question 73

73.

If IJKL is a cyclic parallelogram, then ∠L

(i)

105°
(ii)

90°
(iii)

120°
(iv)

100°
(v)

95°

Question 74

74.

In the given figure, the bisectors of ∠G , ∠H & ∠I of △GHI meet the circumcircle at J , K & L. If ∠G = 54°, find ∠J

(i)

93°
(ii)

68°
(iii)

78°
(iv)

73°
(v)

63°

Question 75

75.

EF is a line segment and H is its mid-point. Three semi-circles are drawn with EH , HF and EF as diameters. G , I and H respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given EG = 6 cm