EduSahara™ Worksheet

Question 1

1.

Which of the following statements are true?

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

(i)

{a,d}
(ii)

{c,d}
(iii)

{e,b,a}
(iv)

{b,a}
(v)

{c,d,a}

Question 2

2.

Which of the following statements are true?

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

(i)

{b,a,c}
(ii)

{d,c}
(iii)

{b,a}
(iv)

{b,d,e}
(v)

{a,c,e}

Question 3

3.

Which of the following statements are true?

a)	The diameter divides the circle into two unequal parts.
b)	A sector is the area enclosed by two radii and a chord.
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)

{c,d,e}
(ii)

{a,c,d}
(iii)

{a,c}
(iv)

{b,d}
(v)

{a,b,e}

Question 4

4.

Which of the following statements are true?

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

(i)

{b,e,c}
(ii)

{a,c}
(iii)

{c,e}
(iv)

{b,e}
(v)

{d,a,c}

Question 5

5.

Which of the following statements are true?

a)	If a trapezium is cyclic, it is a rectangle.
b)	If a rhombus is cyclic, it is a square.
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)

{c,e}
(ii)

{c,e,b}
(iii)

{d,a,b}
(iv)

{a,b}
(v)

{b,e}

Question 6

6.

Which of the following statements are true?

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

(i)

{d,c}
(ii)

{d,c,b}
(iii)

{b,c}
(iv)

{e,a,b}
(v)

{a,b}

Question 7

7.

Which of the following are cyclic quadrilaterals?

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

(i)

{b,d}
(ii)

{a,d,c}
(iii)

{a,c}
(iv)

{c,d}
(v)

{e,f,c}

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 one common tangent can be drawn for any two concentric circles.
c)	A maximum of four common tangents can be drawn touching any two circles.
d)	Atmost two common tangents can be drawn touching any two circles.

(i)

{b,a}
(ii)

{b,c,a}
(iii)

{d,c}
(iv)

{b,d,a}
(v)

{a,c}

Question 9

9.

Which of the following statements are true?

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

(i)

{a,b}
(ii)

{c,a}
(iii)

{d,b}
(iv)

{e,c,a}
(v)

{d,b,a}

Question 10

10.

Which of the following statements are true?

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

(i)

{b,a,c}
(ii)

{b,e,d}
(iii)

{b,a}
(iv)

{a,c,d}
(v)

{e,c}

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

(i)

{b,a,d}
(ii)

{a,d,e}
(iii)

{b,a}
(iv)

{b,c,e}
(v)

{c,d}

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

(i)

{b,a}
(ii)

{b,d}
(iii)

{b,a,c}
(iv)

{a,c,d}
(v)

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

(i)

{b,d}
(ii)

{a,d,b}
(iii)

{c,d}
(iv)

{e,f,b}
(v)

{a,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 quadrilateral.
c)	It is always possible to inscribe a circle in a regular polygon.
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, it must be a kite.

(i)

{d,c}
(ii)

{d,c,a}
(iii)

{e,b,a}
(iv)

{a,c}
(v)

{b,a}

Question 15

15.

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 in the opposite segments are complementary.
d)	Angles subtended by equal length arcs in two circles are equal.

(i)

{c,d,a}
(ii)

{c,a}
(iii)

{c,b,a}
(iv)

{a,b}
(v)

{d,b}

Question 16

16.

The angle subtended by the semicircle at the centre is

(i)

185°
(ii)

210°
(iii)

190°
(iv)

195°
(v)

180°

Question 17

17.

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

(i)

120°
(ii)

100°
(iii)

105°
(iv)

90°
(v)

95°

Question 18

18.

The opposite angles in a cyclic quadrilateral are

(i)

complementary
(ii)

equal
(iii)

supplementary
(iv)

linear pair

Question 19

19.

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

(i)

equilateral triangle
(ii)

acute angled triangle
(iii)

right angle triangle
(iv)

obtuse angled triangle

Question 20

20.

Circles having common centre are called

(i)

concentric circles
(ii)

similar circles
(iii)

intersecting circles
(iv)

congruent circles

Question 21

21.

If two circles are concentric, then

(i)

their centres are same
(ii)

their radii are same
(iii)

their perimeters are same
(iv)

their diameters are same

Question 22

22.

With the vertices of a triangle △EFG as centres, three circles are drawn touching each other externally. If the sides of the triangle are 10 cm , 13 cm and 13 cm , find the radii of the circles

(i)

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

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

10 cm , 10 cm & 13 cm respectively
(iv)

5 cm , 5 cm & 13 cm respectively
(v)

10 cm , 5 cm & 8 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 = 83°, find ∠IHJ

(i)

112°
(ii)

102°
(iii)

127°
(iv)

107°
(v)

97°

Question 24

24.

In the given figure, ∠H = 72° , ∠K = 64° and ∠L = 110°, find ∠KIJ

(i)

71°
(ii)

81°
(iii)

76°
(iv)

96°
(v)

66°

Question 25

25.

Which of the following statements are true?

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

(i)

{e,a,b}
(ii)

{d,c}
(iii)

{d,c,b}
(iv)

{a,b}
(v)

{b,c}

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)	All parallelograms are cyclic.
c)	An isosceles trapezium is cyclic.
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)

{c,d,e}
(ii)

{a,c}
(iii)

{a,b,e}
(iv)

{a,c,d}
(v)

{b,d}

Question 27

27.

Which of the following are not cyclic quadrilaterals?

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

(i)

{a,d}
(ii)

{b,e,d}
(iii)

{c,a,d}
(iv)

{b,e}
(v)

{d,e}

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)

right angle triangle
(ii)

equilateral triangle
(iii)

obtuse angled triangle
(iv)

acute angled triangle

Question 29

29.

Which of the following statements are true?

a)

All diameters of a circle are chords.

b)

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

c)

All chords of a circle are diameters.

d)

22
7
is a rational number.

e)

π
is a rational number.

(i)

{c,a}
(ii)

{c,a,b}
(iii)

{a,b,d}
(iv)

{c,e,d}
(v)

{e,b}

Question 30

30.

If BCDE is a cyclic quadrilateral and ∠B − ∠D = 48°, then ∠D

(i)

81°
(ii)

76°
(iii)

96°
(iv)

71°
(v)

66°

Question 31

31.

If ABCD is a cyclic parallelogram, then ∠D

(i)

100°
(ii)

120°
(iii)

95°
(iv)

90°
(v)

105°

Question 32

32.

Points which lie on the circumference of the circle are called

(i)

Concurrent points
(ii)

Similar points
(iii)

Concyclic points
(iv)

Coincident points
(v)

Cyclic points

Question 33

33.

Two concentric circles are of radii 18 cm and 12 cm. Find the length of the chord of the outer circle that touches the inner circle

(i)

25.83 cm
(ii)

28.83 cm
(iii)

24.83 cm
(iv)

26.83 cm
(v)

27.83 cm

Assignment Key