Write True or False: Give reasons for your answers.
(i) Line segment joining the centre to any point on the circle is a radius of the circle.
(ii) A circle has only finite number of equal chords.
(iii) If a circle is divided into three equal arcs, each is a major arc.
(iv) A chord of a circle, which is twice as long as its radius, is a diameter of the circle.
(v) Sector is the region between the chord and its corresponding arc.
(vi) A circle is a plane figure.

To do:

We have to state whether the given statements are true or false.

Solution:

(i)  We know that,

A line segment joining the centre to any point on the circle is a radius of the circle.

Therefore,

The given statement is true.

 (ii)  We know that,

A circle has infinite number of equal chords.

Therefore,

The given statement is false.  

(iii)  We know that,

If a circle is divided into three equal arcs each is a major arc because each arc measures equal.

Therefore,

The given statement is true. 

(iv)  We know that,

The diameter is defined as twice the length of the radius of a circle. 

Therefore,

The given statement is true.   

(v)  We know that,

A sector of a circle is defined as the portion of a circle that is enclosed between its two radii and the arc adjoining them.

Therefore,

The given statement is true.    

(vi)  We know that,

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Therefore,

The given statement is true.