R d sharma mathematics solutions class 6 Solutions for Chapter 13 circles

Explain the following:

(i) Circle

(ii) Radius

(iii) Centre

(iv) Diameter

(v) Chord

(vi) Interior of a circle.

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

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.

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

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

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?

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

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

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 circle.

(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 ……

In each of the following, state if the statement is true (T) or 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 itslength.