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 = 107°. Find ∠EAD

(i)

34°
(ii)

39°
(iii)

44°
(iv)

64°
(v)

49°

Question 2

2.

In the given figure, HI is a side of regular 5-sided polygon and HJ is a side of regular 6-sided polygon inscribed in a circle with centre O. Find ∠HOI

(i)

72°
(ii)

102°
(iii)

77°
(iv)

82°
(v)

87°

Question 3

3.

In the given figure, CD is a side of regular 10-sided polygon and CE is a side of regular 8-sided polygon inscribed in a circle with centre O. Find ∠CED

(i)

28°
(ii)

18°
(iii)

23°
(iv)

48°
(v)

33°

Question 4

4.

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

(i)

23°
(ii)

33°
(iii)

48°
(iv)

18°
(v)

28°

Question 5

5.

In the given figure, O is the centre of the circle. AB is a diameter of the circle and CD is equal to radius. Find ∠AEB

(i)

70°
(ii)

75°
(iii)

60°
(iv)

65°
(v)

90°

Question 6

6.

In the given figure, O is the centre of the circle. If ∠DGE = 83° and ∠DCF = 65°, find ∠CFE

(i)

42°
(ii)

47°
(iii)

37°
(iv)

32°
(v)

62°

Question 7

7.

In the given figure, O is the centre of the circle, and OK ⟂ GH. If ∠GHI = 42.5°, find ∠GOI

(i)

85°
(ii)

100°
(iii)

115°
(iv)

95°
(v)

90°

Question 8

8.

In the given figure, O is the centre of the circle, and OL ⟂ HI. If ∠HIJ = 42.5°, find ∠OKJ

(i)

47.5°
(ii)

77.5°
(iii)

57.5°
(iv)

62.5°
(v)

52.5°

Question 9

9.

In the given figure, O is the centre of the circle. If ∠DBC = 73.47° and ∠BCD = 75.55°, find the angle ∠BEC

(i)

35.98°
(ii)

60.98°
(iii)

45.98°
(iv)

40.98°
(v)

30.98°

Question 10

10.

Which of the following statements are true?

a)	The diameter is the longest 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 radius is the shortest chord.
e)	A chord divides a circle into two segments.

(i)

{c,e,a}
(ii)

{c,e}
(iii)

{b,a}
(iv)

{d,b,a}
(v)

{a,e}

Question 11

11.

Which of the following statements are true?

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

(i)

{b,a,d}
(ii)

{c,d}
(iii)

{a,d,e}
(iv)

{b,c,e}
(v)

{b,a}

Question 12

12.

Which of the following statements are true?

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

(i)

{c,a}
(ii)

{c,a,b}
(iii)

{c,e,d}
(iv)

{e,b}
(v)

{a,b,d}

Question 13

13.

Which of the following statements are true?

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

(i)

{e,a,b}
(ii)

{a,b}
(iii)

{d,c}
(iv)

{d,c,b}
(v)

{b,c}

Question 14

14.

Which of the following statements are true?

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

(i)

{e,a,b}
(ii)

{b,c}
(iii)

{d,c,b}
(iv)

{d,c}
(v)

{a,b}

Question 15

15.

Which of the following statements are true?

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

(i)

{c,a}
(ii)

{e,c,a}
(iii)

{d,b}
(iv)

{a,b}
(v)

{d,b,a}

Question 16

16.

Which of the following are cyclic quadrilaterals?

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

(i)

{a,b}
(ii)

{d,e,b}
(iii)

{a,f,b}
(iv)

{c,f}
(v)

{b,f}

Question 17

17.

Which of the following statements are true?

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

(i)

{d,c}
(ii)

{a,c}
(iii)

{b,a}
(iv)

{d,c,a}
(v)

{e,b,a}

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

(i)

{b,d}
(ii)

{a,d,b}
(iii)

{a,b}
(iv)

{e,f,b}
(v)

{c,d}

Question 19

19.

Which of the following statements are true?

a)	If a circle can be inscribed in a quadrilateral, it must be a kite.
b)	It is always possible to inscribe a circle in a quadrilateral.
c)	If a circle can be inscribed in a quadrilateral, then it must be a square.
d)	It is always possible to inscribe a circle in a regular polygon.
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,d}
(ii)

{b,e,d}
(iii)

{d,e}
(iv)

{b,e}
(v)

{c,a,d}

Question 20

20.

Which of the following statements are true?

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

(i)

{c,d}
(ii)

{a,d}
(iii)

{b,a}
(iv)

{b,d,a}
(v)

{b,c,a}

Question 21

21.

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

(i)

circumcentre
(ii)

orthocentre
(iii)

excentre
(iv)

incentre
(v)

centroid

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)

4x°
(ii)

x°

2
(iii)

2x°
(iv)

x°

Question 23

23.

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

(i)

minor segment
(ii)

major segment
(iii)

quadrant
(iv)

semi-circle
(v)

minor arc

Question 24

24.

An arc subtends 127° in its alternate segment. The arc is

(i)

minor arc
(ii)

major arc
(iii)

quadrant
(iv)

minor segment
(v)

major segment

Question 25

25.

An arc subtends 69° in its alternate segment. The arc is

(i)

minor arc
(ii)

minor segment
(iii)

major arc
(iv)

major segment
(v)

semi-circle

Question 26

26.

An arc subtends 67° in its alternate segment. Its corresponding major arc subtends what angle in its (major arc) alternate segment?

(i)

143°
(ii)

123°
(iii)

118°
(iv)

113°
(v)

128°

Question 27

27.

An arc subtends 44° in its alternate segment. The angle made by its corresponding major arc at the centre is

(i)

287°
(ii)

272°
(iii)

302°
(iv)

277°
(v)

282°

Question 28

28.

In the given figure, two circles of radii AC = 14.5 cm & BC = 8.9 cm intersect at C & D. The distance between the centres AB = 20 cm, find the length of CD

(i)

11.66 cm
(ii)

10.66 cm
(iii)

12.66 cm
(iv)

13.66 cm
(v)

9.66 cm

Question 29

29.

The angle subtended by the semicircle at the centre is

(i)

195°
(ii)

190°
(iii)

185°
(iv)

210°
(v)

180°

Question 30

30.

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

(i)

90°
(ii)

120°
(iii)

100°
(iv)

95°
(v)

105°

Question 31

31.

Angle subtended by the major arc at the centre is

(i)

complete angle
(ii)

acute angle
(iii)

obtuse angle
(iv)

zero angle
(v)

reflex angle

Question 32

32.

Angle subtended in the major segment is

(i)

zero angle
(ii)

acute angle
(iii)

reflex angle
(iv)

obtuse angle
(v)

complete angle

Question 33

33.

The opposite angles in a cyclic quadrilateral are

(i)

complementary
(ii)

linear pair
(iii)

equal
(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)

equilateral triangle
(ii)

obtuse angled triangle
(iii)

acute angled triangle
(iv)

right angle triangle

Question 35

35.

Circles having common centre are called

(i)

intersecting circles
(ii)

similar circles
(iii)

congruent circles
(iv)

concentric circles

Question 36

36.

If two circles are concentric, then

(i)

their centres are same
(ii)

their perimeters are same
(iii)

their diameters are same
(iv)

their radii are same

Question 37

37.

In the given figure, GHIJ is cyclic quadrilateral. If ∠HIJ = 75°, find ∠FGJ

(i)

105°
(ii)

85°
(iii)

75°
(iv)

80°
(v)

90°

Question 38

38.

In the given figure, AB & CD are diameters of the circle. If ∠ABC = 62.5° find, ∠BOC

(i)

85°
(ii)

70°
(iii)

65°
(iv)

60°
(v)

55°

Question 39

39.

In the given figure, FG & HI are diameters of the circle. If ∠FIH = 34°, find ∠OHG

(i)

49°
(ii)

44°
(iii)

64°
(iv)

39°
(v)

34°

Question 40

40.

In the given figure AC & BC are equal length chords of the circle. Find ∠CAB

(i)

45°
(ii)

50°
(iii)

55°
(iv)

75°
(v)

60°

Question 41

41.

In the given figure, AB is a diameter of the circle with centre O. If ∠BAC = 21.49° and BC = BD, find ∠DCA

(i)

78.51°
(ii)

98.51°
(iii)

73.51°
(iv)

83.51°
(v)

68.51°

Question 42

42.

In the given figure, O is the centre of the circle. If ∠OJL = 47°, find ∠K

(i)

152°
(ii)

167°
(iii)

147°
(iv)

137°
(v)

142°

Question 43

43.

In the given figure, O is the centre of the circle. If ∠EFG = 145°, find ∠OEG

(i)

65°
(ii)

85°
(iii)

60°
(iv)

55°
(v)

70°

Question 44

44.

In the given figure, O is the centre of the circle. If ∠DEO = 29° and ∠OGD = 28°, find ∠EFG

(i)

153°
(ii)

133°
(iii)

128°
(iv)

138°
(v)

123°

Question 45

45.

In the given figure, O is the centre of the circle. If ∠CDO = 12° and ∠OFC = 38°, find ∠DOF

(i)

100°
(ii)

110°
(iii)

105°
(iv)

130°
(v)

115°

Question 46

46.

In the given figure, EFGH is a cyclic quadrilateral. If ∠EGF = 33° and ∠GHF = 47°, find ∠EFG

(i)

130°
(ii)

105°
(iii)

110°
(iv)

115°
(v)

100°

Question 47

47.

In the given figure, EFGH is a cyclic quadrilateral. If ∠EGF = 40° and ∠GHF = 30°, find ∠EHG

(i)

70°
(ii)

85°
(iii)

80°
(iv)

75°
(v)

100°

Question 48

48.

In the given figure, EFGHIJ is a regular hexagon. Find ∠EGF

(i)

60°
(ii)

35°
(iii)

30°
(iv)

40°
(v)

45°

Question 49

49.

In the given figure, EFGHIJ is a regular hexagon. Find ∠EHG

(i)

65°
(ii)

70°
(iii)

90°
(iv)

75°
(v)

60°

Question 50

50.

With the vertices of a triangle △CDE as centres, three circles are drawn touching each other externally. If the sides of the triangle are 9 cm , 15 cm and 12 cm , find the radii of the circles

(i)

3 cm , 11 cm & 9 cm respectively
(ii)

3 cm , 6 cm & 9 cm respectively
(iii)

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

8 cm , 11 cm & 14 cm respectively
(v)

3 cm , 6 cm & 14 cm respectively

Question 51

51.

O is the centre of the circle. If ∠EFD = 67°, find the angle ∠OED

(i)

38°
(ii)

28°
(iii)

53°
(iv)

33°
(v)

23°

Question 52

52.

In the given figure, GHIJ is a cyclic quadrilateral. If ∠GHJ = 65° and ∠HIG = 49°, find ∠JGH

(i)

76°
(ii)

66°
(iii)

96°
(iv)

81°
(v)

71°

Question 53

53.

LM is the perpendicular bisector of side JK of △IJK. Given ∠IJK = 58° and ∠LIK = 45° , find ∠IKJ

(i)

32°
(ii)

62°
(iii)

42°
(iv)

37°
(v)

47°

Question 54

54.

In the given figure, △HEF is a scalene triangle. GE bisects ∠HEF. Similarly FG bisects ∠EFH. Given ∠FHE = 92°, find ∠FGE

(i)

166°
(ii)

146°
(iii)

141°
(iv)

151°
(v)

136°

Question 55

55.

In the given figure, △MIJ is a scalene triangle. KI & LI trisect ∠MIJ. Similarly JK & JL trisect ∠IJM. Given ∠JMI = 84°, find ∠JKI

(i)

153°
(ii)

158°
(iii)

148°
(iv)

163°
(v)

178°

Question 56

56.

In the given figure, △EAB is a scalene triangle. CA & DA trisect ∠EAB. Similarly BC & BD trisect ∠ABE. Given ∠BEA = 75°, find ∠BDA

(i)

110°
(ii)

120°
(iii)

140°
(iv)

115°
(v)

125°

Question 57

57.

In the given figure, ∠HJK = 13° and ∠HLK = 34°, find ∠JHK

(i)

43°
(ii)

58°
(iii)

48°
(iv)

53°
(v)

73°

Question 58

58.

In the given figure, ∠HJK = 10° and ∠HLK = 26°, find ∠IKH

(i)

95°
(ii)

85°
(iii)

80°
(iv)

110°
(v)

90°

Question 59

59.

In the given figure, CD , DE , EF and FG are chords and CF , DG are diameters passing through the centre O. If ∠COD = 66°. Find ∠DEF

(i)

138°
(ii)

153°
(iii)

133°
(iv)

128°
(v)

123°

Question 60

60.

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

a)	∠HKI = 30°
b)	∠GOL = 60°
c)	∠HOJ = 120°
d)	∠LJI = 90°
e)	∠GIH = 60°

(i)

{a,b,c,d}
(ii)

{e,d,a}
(iii)

{e,c}
(iv)

{e,a}
(v)

{e,b}

Question 61

61.

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

(i)

72°
(ii)

77°
(iii)

102°
(iv)

82°
(v)

87°

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)

40° & 140°
(ii)

60° & 120°
(iii)

50° & 130°
(iv)

45° & 135°
(v)

30° & 150°

Question 63

63.

In the given figure, IJKM is a cyclic quadrilateral where JK and JI are produced to L and H respectively. If ∠HIM = 92°, find ∠LKM

(i)

118°
(ii)

103°
(iii)

98°
(iv)

88°
(v)

93°

Question 64

64.

In the given figure, ∠E = 74° , ∠H = 71° and ∠I = 104°, find ∠HFG

(i)

99°
(ii)

74°
(iii)

79°
(iv)

84°
(v)

69°

Question 65

65.

Which of the following statements are true?

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

(i)

{d,c,b}
(ii)

{e,a,b}
(iii)

{b,c}
(iv)

{a,b}
(v)

{d,c}

Question 66

66.

Which of the following statements are true?

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

(i)

{e,c}
(ii)

{b,c,d}
(iii)

{a,b}
(iv)

{a,b,c}
(v)

{a,e,d}

Question 67

67.

Which of the following are not cyclic quadrilaterals?

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

(i)

{b,e,d}
(ii)

{d,e}
(iii)

{c,a,d}
(iv)

{b,e}
(v)

{a,d}

Question 68

68.

Which of the following statements are true?

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

(i)

{a,b,c}
(ii)

{b,c,e}
(iii)

{a,b}
(iv)

{a,d,e}
(v)

{d,c}

Question 69

69.

In triangle IJK, if a circle is drawn with JK as diameter and if it passes through I it is a

(i)

right angle triangle
(ii)

obtuse angled triangle
(iii)

acute angled triangle
(iv)

equilateral triangle

Question 70

70.

Which of the following statements are true?

a)

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

b)

All chords of a circle are diameters.

c)

π
is a rational number.

d)

22
7
is a rational number.

e)

All diameters of a circle are chords.

(i)

{a,d,e}
(ii)

{b,a}
(iii)

{b,c,e}
(iv)

{b,a,d}
(v)

{c,d}

Question 71

71.

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

a)	∠C + ∠ODE = 90°
b)	∠C + ∠DOE = 180°
c)	∠C + ∠ODE + ∠OED = 2 ∠C
d)	∠C + ∠ODE = 120°
e)	∠C + ∠OED = 90°

(i)

{d,b,a}
(ii)

{c,e}
(iii)

{b,a}
(iv)

{a,e}
(v)

{c,e,a}

Question 72

72.

If ABCD is a cyclic quadrilateral and ∠A − ∠C = 20°, then ∠C

(i)

80°
(ii)

90°
(iii)

95°
(iv)

85°
(v)

110°

Question 73

73.

If ABCD is a cyclic parallelogram, then ∠D

(i)

90°
(ii)

120°
(iii)

100°
(iv)

105°
(v)

95°

Question 74

74.

In the given figure, the bisectors of ∠B , ∠C & ∠D of △BCD meet the circumcircle at E , F & G. If ∠B = 65°, find ∠E

(i)

87.5°
(ii)

62.5°
(iii)

57.5°
(iv)

72.5°
(v)

67.5°

Question 75

75.

BC is a line segment and E is its mid-point. Three semi-circles are drawn with BE , EC and BC as diameters. D , F and E respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given BD = 7 cm