Question

Write True or False: Give reasons for your Solution:s.
(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.


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Answer 1

$\huge\star{\pink{\underline{\bold{\mathrm{Explanation:}}}}}$

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(i) Line segment joining the centre to any point on the circle is a radius of the circle.

$\hookrightarrow$ (i) $\mathrm{\red{</u></strong><strong><u>True</u></strong><strong><u>}}$

$\leadsto$ Any line segment drawn from the centre of the circle to any point on it is the radius of the circle and will be of equal length.

(ii) A circle has only finite number of equal chords.

$\hookrightarrow$ (ii) $\mathrm{\red{False}}$ 

$\leadsto$ There can be infinite numbers of equal chords of a circle.

(iii) If a circle is divided into three equal arcs, each is a major arc.

$\hookrightarrow$ (iii)$\mathrm{\red{False}}$

$\leadsto$ For unequal arcs, there can be major and minor arcs. So, equal arcs on a circle cannot be said as a major arc or a minor arc.

(iv) A chord of a circle, which is twice as long as its radius, is a diameter of the circle.

$\hookrightarrow$ (iv) $\mathrm{\red{True}}$

$\leadsto$ Any chord whose length is twice as long as the radius of the circle always passes through the centre of the circle and thus, it is known as the diameter of the circle.

(v) Sector is the region between the chord and its corresponding arc.

$\hookrightarrow$ (v)  $\mathrm{\red{False}}$

$\leadsto$ A sector is a region of a circle between the arc and the two radii of the circle.

(vi) A circle is a plane figure.

$\hookrightarrow$ (vi) $\mathrm{\red{True}}$

$\leadsto$ A circle is a 2d figure and it can be drawn on a plane.

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Answer 2

$\huge \underline \mathbb {SOLUTION:-}$

(i) True

• Any line segment drawn from the centre of the circle to any point on it is the radius of the circle and will be of equal length.

(ii) False

• There can be infinite numbers of equal chords of a circle.

(iii) False

• For unequal arcs, there can be major and minor arcs. So, equal arcs on a circle cannot be said as a major arc or a minor arc.

(iv) True

• Any chord whose length is twice as long as the radius of the circle always passes through the centre of the circle and thus, it is known as the diameter of the circle.

(v) False

• A sector is a region of a circle between the arc and the two radii of the circle.

(vi) True

• A circle is a 2d figure and it can be drawn on a plane.