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.

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Solution

(i) T
(ii) F
(iii) F
(iv) F
(v) T
(vi) T
(vii) F
(viii) F
(ix) T

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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.

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

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

(vi) A circle is a plane figure.

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