Q. 25.0( 3 Votes )

# Write True/False. Give reason also 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 parts, each is a major are.

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

(v) A circle is a plane figure.

(vi) The collection of those points in a plane, which are at a fixed distance from a fixed point in the plane, is called a diameter.

(vii) The chord on which centre lies is called radius.

Answer :

(i) True

We know that the constant distance is radius of a circle.

The line segment joining the centre to any point on the circle has constant distance.

∴ Line segment joining the centre to any point on the circle is a radius of the circle.

(ii) False

In a circle, infinitely many diameters can be drawn.

A diameter is the longest chord.

∴ a circle has infinitely many chords.

(iii) False

When a circle is divided into three equal parts, each part will be less than a semicircle.

(iv) True

We know that diameter is twice the radius i.e. d = 2r.

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

(v) True

A circle is drawn on a plane which divides it into three parts.

∴ A circle is a plane figure.

(vi) False

The collection of those points in a plane, which are at a fixed distance from a fixed point in the plane, is called a circle.

(vii) False

We know that if any chord passes through the centre of the circle then it is called the diameter of the circle.

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Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Rajasthan Board Mathematics