EduSahara™ Worksheet

Question 1

1.

Which of the following statements are true?

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

(i)

{d,c}
(ii)

{b,a}
(iii)

{e,b,a}
(iv)

{d,c,a}
(v)

{a,c}

Question 2

2.

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)	Equal length chords subtend equal angles at the centre of the circle.
d)	The longest chord of the circle passes through the centre of the circle.
e)	No two chords bisects each other.

(i)

{b,a,c}
(ii)

{a,c,d}
(iii)

{b,a}
(iv)

{e,c}
(v)

{b,e,d}

Question 3

3.

Which of the following statements are true?

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

(i)

{b,c,e}
(ii)

{a,d,e}
(iii)

{d,c}
(iv)

{a,b,c}
(v)

{a,b}

Question 4

4.

Which of the following statements are true?

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

(i)

{b,e,c}
(ii)

{b,e}
(iii)

{d,a,c}
(iv)

{c,e}
(v)

{a,c}

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 kite is cyclic, it is a square.
e)	If a rhombus is cyclic, it is a square.

(i)

{d,a,c}
(ii)

{b,e,c}
(iii)

{b,e}
(iv)

{c,e}
(v)

{a,c}

Question 6

6.

Which of the following statements are true?

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

(i)

{a,d}
(ii)

{b,e,d}
(iii)

{d,e}
(iv)

{b,e}
(v)

{c,a,d}

Question 7

7.

Which of the following are cyclic quadrilaterals?

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

(i)

{e,f,a}
(ii)

{c,b,a}
(iii)

{c,a}
(iv)

{d,b}
(v)

{a,b}

Question 8

8.

Which of the following statements are true?

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

(i)

{a,b}
(ii)

{c,d,a}
(iii)

{c,a}
(iv)

{d,b}
(v)

{c,b,a}

Question 9

9.

Which of the following statements are true?

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

(i)

{a,b}
(ii)

{d,a,b}
(iii)

{c,e,b}
(iv)

{b,e}
(v)

{c,e}

Question 10

10.

Which of the following statements are true?

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

(i)

{a,b,c}
(ii)

{a,d,e}
(iii)

{b,c,e}
(iv)

{d,c}
(v)

{a,b}

Question 11

11.

Which of the following statements are true?

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

(i)

{a,c,d}
(ii)

{c,d,e}
(iii)

{b,d}
(iv)

{a,c}
(v)

{a,b,e}

Question 12

12.

Which of the following statements are true?

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

(i)

{c,a,b}
(ii)

{c,a}
(iii)

{c,d}
(iv)

{c,b}
(v)

{a,b,d}

Question 13

13.

Which of the following statements are true?

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

(i)

{a,b}
(ii)

{b,e}
(iii)

{c,e}
(iv)

{d,f,b}
(v)

{a,e,b}

Question 14

14.

Which of the following statements are true?

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

{c,e}
(iii)

{d,a,c}
(iv)

{b,e,c}
(v)

{b,e}

Question 15

15.

Which of the following statements are true?

a)	Angles in the opposite segments are complementary.
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 supplementary.

(i)

{a,b}
(ii)

{b,d}
(iii)

{a,c,b}
(iv)

{c,d}
(v)

{a,d,b}

Question 16

16.

The angle subtended by the semicircle at the centre is

(i)

180°
(ii)

185°
(iii)

195°
(iv)

190°
(v)

210°

Question 17

17.

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

(i)

120°
(ii)

100°
(iii)

105°
(iv)

95°
(v)

90°

Question 18

18.

The opposite angles in a cyclic quadrilateral are

(i)

equal
(ii)

complementary
(iii)

linear pair
(iv)

supplementary

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)

equilateral triangle
(iii)

obtuse angled triangle
(iv)

right angle triangle

Question 20

20.

Circles having common centre are called

(i)

similar circles
(ii)

intersecting circles
(iii)

congruent circles
(iv)

concentric circles

Question 21

21.

If two circles are concentric, then

(i)

their centres are same
(ii)

their diameters are same
(iii)

their radii are same
(iv)

their perimeters are same

Question 22

22.

With the vertices of a triangle △ABC as centres, three circles are drawn touching each other externally. If the sides of the triangle are 13 cm , 17 cm and 14 cm , find the radii of the circles

(i)

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

10 cm , 13 cm & 14 cm respectively
(iii)

5 cm , 13 cm & 9 cm respectively
(iv)

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

5 cm , 8 cm & 9 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)

94°
(iii)

104°
(iv)

89°
(v)

119°

Question 24

24.

In the given figure, ∠G = 80° , ∠J = 70° and ∠K = 108°, find ∠JHI

(i)

88°
(ii)

78°
(iii)

108°
(iv)

83°
(v)

93°

Question 25

25.

Which of the following statements are true?

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

(i)

{d,c,a}
(ii)

{d,c}
(iii)

{e,b,a}
(iv)

{a,c}
(v)

{b,a}

Question 26

26.

Which of the following statements are true?

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

(i)

{a,b}
(ii)

{c,d}
(iii)

{b,d,e}
(iv)

{a,b,d}
(v)

{a,c,e}

Question 27

27.

Which of the following are not cyclic quadrilaterals?

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

(i)

{c,d,a}
(ii)

{e,b,a}
(iii)

{a,d}
(iv)

{b,a}
(v)

{c,d}

Question 28

28.

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

(i)

acute angled triangle
(ii)

equilateral triangle
(iii)

obtuse angled triangle
(iv)

right angle triangle

Question 29

29.

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)

22
7
is a rational number.

d)

π
is a rational number.

e)

All diameters of a circle are chords.

(i)

{b,d,e}
(ii)

{d,c}
(iii)

{b,a}
(iv)

{a,c,e}
(v)

{b,a,c}

Question 30

30.

If GHIJ is a cyclic quadrilateral and ∠G − ∠I = 2°, then ∠I

(i)

99°
(ii)

119°
(iii)

89°
(iv)

94°
(v)

104°

Question 31

31.

If IJKL is a cyclic parallelogram, then ∠L

(i)

120°
(ii)

100°
(iii)

95°
(iv)

90°
(v)

105°

Question 32

32.

Points which lie on the circumference of the circle are called

(i)

Concyclic points
(ii)

Coincident points
(iii)

Concurrent points
(iv)

Cyclic points
(v)

Similar points

Question 33

33.

Two concentric circles are of radii 24 cm and 10 cm. Find the length of the chord of the outer circle that touches the inner circle

(i)

42.63 cm
(ii)

45.63 cm
(iii)

43.63 cm
(iv)

41.63 cm
(v)

44.63 cm

Assignment Key