EduSahara™ Worksheet

Question 1

1.

Which of the following statements are true?

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

(i)

{c,d}
(ii)

{e,a,c}
(iii)

{a,c}
(iv)

{b,d}
(v)

{b,d,c}

Question 2

2.

Which of the following statements are true?

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

(i)

{e,c}
(ii)

{a,b}
(iii)

{a,e,d}
(iv)

{a,b,c}
(v)

{b,c,d}

Question 3

3.

Which of the following statements are true?

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

(i)

{d,b}
(ii)

{c,d,e}
(iii)

{c,a,b}
(iv)

{a,b,e}
(v)

{c,a}

Question 4

4.

Which of the following statements are true?

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

(i)

{a,d}
(ii)

{c,d}
(iii)

{c,d,a}
(iv)

{e,b,a}
(v)

{b,a}

Question 5

5.

Which of the following statements are true?

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

(i)

{a,c}
(ii)

{c,d}
(iii)

{e,a,c}
(iv)

{b,d,c}
(v)

{b,d}

Question 6

6.

Which of the following statements are true?

a)	Infinite circles can be drawn passing through three 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)	Atmost one circle can be drawn passing through three non-collinear points.
e)	Only one circle can be drawn with a centre.

(i)

{e,a,b}
(ii)

{c,d,b}
(iii)

{c,d}
(iv)

{a,b}
(v)

{b,d}

Question 7

7.

Which of the following are cyclic quadrilaterals?

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

(i)

{b,d}
(ii)

{e,f,b}
(iii)

{a,b}
(iv)

{c,d}
(v)

{a,d,b}

Question 8

8.

Which of the following statements are true?

a)	Atmost three common tangents can be drawn touching two circles which touch each other.
b)	Atmost two common tangents can be drawn touching any two circles.
c)	Atmost one common tangent can be drawn for any two concentric circles.
d)	A maximum of four common tangents can be drawn touching any two circles.

(i)

{b,d,a}
(ii)

{a,d}
(iii)

{c,d}
(iv)

{b,a}
(v)

{b,c,a}

Question 9

9.

Which of the following statements are true?

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

(i)

{b,e}
(ii)

{c,e}
(iii)

{d,a,c}
(iv)

{a,c}
(v)

{b,e,c}

Question 10

10.

Which of the following statements are true?

a)	Only one tangent can be drawn through a point on a circle.
b)	The sides of a triangle can be tangents to a circle.
c)	Two tangents to a circle always intersect.
d)	Atmost one tangent can be drawn through a point inside the circle.
e)	Only two tangents can be drawn from a point outside the circle.

(i)

{a,b,e}
(ii)

{c,a}
(iii)

{c,a,b}
(iv)

{c,d,e}
(v)

{d,b}

Question 11

11.

Which of the following statements are true?

a)	If two tangents are perpendicular, they form a right angled triangle with their points of contact with the circle and their point of intersection.
b)	If two tangents to a circle intersect, their points of contact with the circle together with their point of intersection form an isosceles triangle.
c)	A line parallel to a tangent is a secant.
d)	If two tangents are parallel, the distance between them is equal to the diameter of the circle.
e)	Two different tangents can meet at a point on the circle.

(i)

{a,b,d}
(ii)

{e,b}
(iii)

{c,a,b}
(iv)

{c,e,d}
(v)

{c,a}

Question 12

12.

Which of the following statements are true?

a)	If two circles touch each other internally, there is only one common tangent.
b)	If two circles touch each other externally, there is only one common tangent.
c)	If two circles intersect, then two common tangents can be drawn.
d)	There exists four common tangents for any two non-intersecting circles.

(i)

{b,a}
(ii)

{b,d}
(iii)

{a,c,d}
(iv)

{b,c}
(v)

{b,a,c}

Question 13

13.

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

{a,b}
(iii)

{c,e}
(iv)

{d,f,b}
(v)

{a,e,b}

Question 14

14.

Which of the following statements are true?

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

(i)

{a,b}
(ii)

{c,a}
(iii)

{d,b}
(iv)

{d,b,a}
(v)

{e,c,a}

Question 15

15.

Which of the following statements are true?

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

(i)

{a,b,c}
(ii)

{b,d}
(iii)

{a,d,c}
(iv)

{c,d}
(v)

{a,c}

Question 16

16.

The angle subtended by the semicircle at the centre is

(i)

195°
(ii)

180°
(iii)

190°
(iv)

185°
(v)

210°

Question 17

17.

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

(i)

105°
(ii)

120°
(iii)

95°
(iv)

100°
(v)

90°

Question 18

18.

The opposite angles in a cyclic quadrilateral are

(i)

supplementary
(ii)

complementary
(iii)

linear pair
(iv)

equal

Question 19

19.

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

(i)

acute angled triangle
(ii)

right angle triangle
(iii)

equilateral triangle
(iv)

obtuse angled triangle

Question 20

20.

Circles having common centre are called

(i)

intersecting circles
(ii)

similar circles
(iii)

congruent circles
(iv)

concentric circles

Question 21

21.

If two circles are concentric, then

(i)

their diameters are same
(ii)

their perimeters are same
(iii)

their centres are same
(iv)

their radii are same

Question 22

22.

With the vertices of a triangle △DEF as centres, three circles are drawn touching each other externally. If the sides of the triangle are 8 cm , 14 cm and 12 cm , find the radii of the circles

(i)

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

3 cm , 5 cm & 9 cm respectively
(iii)

8 cm , 10 cm & 14 cm respectively
(iv)

3 cm , 10 cm & 9 cm respectively
(v)

3 cm , 5 cm & 14 cm respectively

Question 23

23.

In the given figure, FGHJ is a cyclic quadrilateral where GH and GF are produced to I and E respectively. If ∠EFJ = 91°, find ∠IHJ

(i)

99°
(ii)

119°
(iii)

104°
(iv)

94°
(v)

89°

Question 24

24.

In the given figure, ∠C = 55° , ∠F = 69° and ∠G = 115°, find ∠FDE

(i)

89°
(ii)

69°
(iii)

64°
(iv)

74°
(v)

59°

Question 25

25.

Which of the following statements are true?

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

(i)

{c,e}
(ii)

{d,a,b}
(iii)

{a,b}
(iv)

{b,e}
(v)

{c,e,b}

Question 26

26.

Which of the following statements are true?

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

(i)

{b,d,e}
(ii)

{b,a,c}
(iii)

{d,c}
(iv)

{a,c,e}
(v)

{b,a}

Question 27

27.

Which of the following are not cyclic quadrilaterals?

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

(i)

{a,b}
(ii)

{b,e}
(iii)

{c,e}
(iv)

{d,a,b}
(v)

{c,e,b}

Question 28

28.

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)

obtuse angled triangle
(iii)

right angle triangle
(iv)

equilateral triangle

Question 29

29.

Which of the following statements are true?

a)

All chords of a circle are diameters.

b)

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

c)

22
7
is a rational number.

d)

All diameters of a circle are chords.

e)

π
is a rational number.

(i)

{a,b,c}
(ii)

{a,e,d}
(iii)

{a,b}
(iv)

{e,c}
(v)

{b,c,d}

Question 30

30.

If CDEF is a cyclic quadrilateral and ∠C − ∠E = 14°, then ∠E

(i)

93°
(ii)

98°
(iii)

83°
(iv)

113°
(v)

88°

Question 31

31.

If IJKL is a cyclic parallelogram, then ∠L

(i)

95°
(ii)

120°
(iii)

90°
(iv)

105°
(v)

100°

Question 32

32.

Points which lie on the circumference of the circle are called

(i)

Cyclic points
(ii)

Similar points
(iii)

Concurrent points
(iv)

Coincident points
(v)

Concyclic points

Question 33

33.

Two concentric circles are of radii 20 cm and 13 cm. Find the length of the chord of the outer circle that touches the inner circle

(i)

29.40 cm
(ii)

30.40 cm
(iii)

28.40 cm
(iv)

31.40 cm
(v)

32.40 cm

Assignment Key