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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.
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