EduSahara™ Worksheet

Question 1

1.

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

(i)

{a,e}
(ii)

{c,e,a}
(iii)

{d,b,a}
(iv)

{c,e}
(v)

{b,a}

Question 2

2.

△DEF is inscribed in a circle with centre O. If ∠DOE = 133° and ∠EOF = 149°, find ∠EFD

(i)

71.5°
(ii)

76.5°
(iii)

96.5°
(iv)

81.5°
(v)

66.5°

Question 3

3.

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

(i)

294°
(ii)

264°
(iii)

269°
(iv)

279°
(v)

274°

Question 4

4.

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

a)	∠J + ∠OKL = 120°
b)	∠J + ∠OLK = 90°
c)	∠J + ∠OKL + ∠OLK = 2 ∠J
d)	∠J + ∠KOL = 180°
e)	∠J + ∠OKL = 90°

(i)

{a,b}
(ii)

{c,e}
(iii)

{d,a,b}
(iv)

{c,e,b}
(v)

{b,e}

Question 5

5.

O is the centre of the circle. If ∠IOH = 110° and ∠JOH = 97°, find ∠IHJ

(i)

86.5°
(ii)

106.5°
(iii)

81.5°
(iv)

76.5°
(v)

91.5°

Question 6

6.

If the radius of a circle is 14 cm, what is its diameter?

(i)

26 cm
(ii)

28 cm
(iii)

30 cm
(iv)

27 cm
(v)

29 cm

Question 7

7.

In the given figure, △BCD is an isosceles such that BC = BD. Given BO = 12 cm, BC = BD = 21 cm, find CD

(i)

22.33 cm
(ii)

19.33 cm
(iii)

21.33 cm
(iv)

18.33 cm
(v)

20.33 cm

Question 8

8.

The radii of the circle are

(i)

HI

,

IJ

,

JK

,

KL

,

LH

,

MI
(ii)

IJ

,

JK

,

KL

,

LH
(iii)

HI

,

IJ

,

JK

,

KL

,

LH
(iv)

HI

,

IJ

,

JK

,

KL

,

LH

,

JL
(v)

MH

,

MI

,

MJ

,

MK

,

ML

Question 9

9.

If FGHI is a cyclic parallelogram, then ∠I

(i)

120°
(ii)

105°
(iii)

95°
(iv)

90°
(v)

100°

Question 10

10.

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

(i)

20°
(ii)

25°
(iii)

30°
(iv)

35°
(v)

50°

Question 11

11.

A line which touches a circle at only one point is called a

(i)

diameter
(ii)

quadrant
(iii)

chord
(iv)

centre
(v)

tangent

Question 12

12.

In the given figure, O is the centre of the circle. If ∠IOJ = 86° and ∠JKM = 86°, find ∠LIO

(i)

44°
(ii)

39°
(iii)

54°
(iv)

69°
(v)

49°

Question 13

13.

In triangle JKL, if a circle is drawn with KL as diameter and if it passes through J it is a

(i)

acute angled triangle
(ii)

obtuse angled triangle
(iii)

right angle triangle
(iv)

equilateral triangle

Question 14

14.

Find the side of the square in the following figure if the radius of the circle is 13.00 cm.

(i)

19.38 cm
(ii)

18.38 cm
(iii)

20.38 cm
(iv)

16.38 cm
(v)

17.38 cm

Question 15

15.

In the given figure, O is the centre of the circle , chord BC is equal to chord CD and AC is a diameter. If ∠DAC = 47° find ∠BCD

(i)

116°
(ii)

101°
(iii)

86°
(iv)

91°
(v)

96°

Question 16

16.

Which of the following statements are true?

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

(i)

{c,d}
(ii)

{a,d,e}
(iii)

{b,a,d}
(iv)

{b,a}
(v)

{b,c,e}

Question 17

17.

In the given figure, a pentagon is inscribed in a circle with centre O. Given AB = BC = CD , ∠BCD = 101° and ∠EAB = 114°. Find ∠CDE

(i)

105.5°
(ii)

115.5°
(iii)

135.5°
(iv)

120.5°
(v)

110.5°

Question 18

18.

In the given figure, DEFH is a cyclic quadrilateral where EF and ED are produced to G and C respectively. If ∠CDH = 91°, find ∠GFH

(i)

104°
(ii)

89°
(iii)

94°
(iv)

99°
(v)

119°

Question 19

19.

Which of the following statements are true?

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

(i)

{c,d}
(ii)

{e,a,b}
(iii)

{a,b}
(iv)

{c,d,b}
(v)

{b,d}

Question 20

20.

In the given figure, O is the centre of the circle , chord AD is equal to chord DC. If ∠AOB = 87° and ∠ADC = 116°, find ∠BCD

(i)

80.5°
(ii)

105.5°
(iii)

75.5°
(iv)

90.5°
(v)

85.5°

Question 21

21.

In the given figure, EF & GH are diameters of the circle. If ∠EFG = 61° find, ∠FOG

(i)

58°
(ii)

63°
(iii)

68°
(iv)

73°
(v)

88°

Question 22

22.

In the given figure, IJ , JK , KL and LM are chords and IL , JM are diameters passing through the centre O. If ∠IOJ = 77°. Find ∠JKL

(i)

133.5°
(ii)

158.5°
(iii)

143.5°
(iv)

138.5°
(v)

128.5°

Question 23

23.

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

(i)

48°
(ii)

18°
(iii)

28°
(iv)

23°
(v)

33°

Question 24

24.

Which of the following are not cyclic quadrilaterals?

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

(i)

{a,b}
(ii)

{d,c,b}
(iii)

{d,c}
(iv)

{e,a,b}
(v)

{b,c}

Question 25

25.

In the given figure, O is the centre of the circle. If ∠BCD = 124.5°, find ∠DOB + ∠BAD

(i)

304.5°
(ii)

309.5°
(iii)

314.5°
(iv)

334.5°
(v)

319.5°

Assignment Key