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#### Page No 14.4:

#### Question 1:

Explain the following:

(i) Circle

(ii) Radius

(iii) Centre

(iv) Diameter

(v) Chord

(vi) Interior of a circle

#### Answer:

(i) A circle is a set of all those points in a plane, whose distance from a fixed point remains constant.

(ii) Radius of a circle is a line segment with one end at its centre and the other end on the circle. (It is the constant distance between all the points on the circle and its centre.)

(iii) The centre of a circle is that fixed point from which all points remain at a constant distance.

(iv) Diameter of a circle is a line segment passing through the centre of a circle, and having its end points on the circle.

(v) A chord of a circle is a line segment with its end points lying on the circle.

(vi) Interior of a circle is a set of all those points which lie inside the circle.

#### Page No 14.4:

#### Question 2:

Take a point on your notebook and draw circle of radii 4 cm, 3 cm and 6.5 cm, each having the sme centre *O*.

#### Answer:

The given figure shows circles of radii 4 cm, 3 cm and 6.5 cm, respectively.

#### Page No 14.4:

#### Question 3:

Draw a circle with centre *O* and any radius. Draw *AC* and *BD* two perpendicular diameters of the circle. Join *AB, BC, CD* and* DA.*

#### Answer:

The figure is shown below -

#### Page No 14.4:

#### Question 4:

Draw a circle with centre* O* and radius 6 cm. Mark points *P, Q, R* such that

(i) *P* lies on the circle,

(ii) *Q* lies in the interior of the circle, and

(iii)* R* lies in the exterior of the circle,

Rewrite each of the following statements using the correct symbol (=,< or >):

(i) *OQ*....5 cm

(ii) *OP*....5 cm

(iii) *OR* ....5 cm

#### Answer:

The given figure shows the points P, Q and R such that

(i) P lies on the circle.

(ii) Q lies in the interior of the circle.

(iii) R lies on the exterior of the circle.

(i) OQ < 5 cm

(ii) OP = 5 cm

(iii) OR> 5 cm

#### Page No 14.4:

#### Question 5:

Take two points *A* and *B* on the page of your note book. Draw a circle with centre *A* which passes through *B*.

#### Answer:

The figure is shown below -

#### Page No 14.4:

#### Question 6:

Draw a semi-circle with centre *O *and radius 5 cm. Is the diameter that determines the semi-circle, a part of the semi-circle?

#### Answer:

The semi -circle with centre O and radius 5 cm is shown below -

The end point of a diameter of a circle divides it into two equal parts, and each part is called a semi circle. So, it is not the diameter, but end points of the diameter that determines the semi circle or a part of the semi circle.

#### Page No 14.4:

#### Question 7:

The diameter of a circle is 14 cm, find its radius.

#### Answer:

The radius of a circle is half of its diameter.

Therefore, the radius = diameter/2

#### Page No 14.4:

#### Question 8:

Given a circle with centre *O *and radius 2.5 cm, what is the length of the longest chord of the circle.

#### Answer:

The diameter of a circle is its longest chord.

The diameter of a circle is twice of its radius.

∴ Length of the longest chord is: 2 ⨯ 2.5 = 5 cm

#### Page No 14.5:

#### Question 9:

Fill in the blanks:

(i) The diameter of a circle is .....times its radius.

(ii) The diameter of a circle is the ..... chord of the cirlce.

(iii) The diameter of a circle pass through......

(iv) A chord of a circle is a line segment with its end points on the....

(v) If we join any two points on a circle by a line segment, we obtain.... of the circle.

(vi) A radius of a circle is a line segment with one end at .... and the other end at.....

(vii) All radii of a circle are.....

(viii) The diameters of a circle are

(ix) The total number of diameters of a circle is .....

(x) Every point on a circle is .....from its centre.

(xi) A chord of a circle contains exactly ...... points of the circle.

(xii) A diameter is the longest.......

(xiii) Concentric circles are circles having.......

#### Answer:

(i) two

(ii) longest

(iii) the centre of the circle

(iv) circle

(v) chord

(vi) the centre, on the circle

(vii) equal

(viii) concurrent

(ix) infinite

(x) equidistant

(xi) two

(xii) chord

(xiii) the same centre point

#### Page No 14.5:

#### Question 10:

In each of the following, state if the statement is true (T) of false (F);

(i) Every circle has a centre.

(ii) The centre of a circle is a point of the circle.

(iii) Any two radii of a circle make up a diameter.

(iv) Every chord of a circle is parallel to some diameter of the circle.

(v) A circle is symmetric about each of its diameters.

(vi) The diameter is twice the radius.

(vii) A radius is a chord of the circle.

(viii) Concentric circles have the same radii.

(ix) The nearer a chord to the centre of a circle, the longer is its length.

#### Answer:

(i) T

(ii) F

(iii) F

(iv) F

(v) T

(vi) T

(vii) F

(viii) F

(ix) T

#### Page No 14.5:

#### Question 1:

A circle of radius *r* cm has diameter of length

(a) *r *cm

(b) 2*r* cm

(c) 4*r* cm

(d) $\frac{r}{2}$ cm

#### Answer:

(b) 2r cm

(Diameter = 2x radius)

#### Page No 14.5:

#### Question 2:

A chord of a circle passing through its centre is equal to its

(a) radius

(b) diameter

(c) circumference

(d) none of these

#### Answer:

(b) Diameter

#### Page No 14.5:

#### Question 3:

The total number of diameters of a circle is

(a) 1

(b) 2

(c) 4

(d) uncountable number

#### Answer:

(d) An uncountable number

The number of points in a circle is infinite. So, the number of diametrically opposite points in a circle is also infinite. Hence, the number of diameters of a circle is uncountable.

#### Page No 14.5:

#### Question 4:

By joining any two points on a circle, we obtain its

(a) radius

(b) diameter

(c) chord

(d) circumference

#### Answer:

(c) Chord

#### Page No 14.6:

#### Question 5:

The longest chord of a circle is equal to its

(a) radius

(b) diameter

(c) circumference

(d) perimeter

#### Answer:

(b) Diameter

#### Page No 14.6:

#### Question 6:

How many circles can be drawn to pass through two given points?

(a) 1

(b) 2

(c) 0

(d) As many as possible

#### Answer:

(d) As many as possible

(Three non-collinear points define one specific circle. From any two given points, infinite number of circles can be drawn.)

#### Page No 14.6:

#### Question 7:

How many circles can be drawn to pass through three non-collinear points?

(a) 1

(b) 2

(c) 0

(d) As many as possible

#### Answer:

(a) 1

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