Q2 of 63 Page 139

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.

(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.


More from this chapter

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1

Fill in the blank:

(i) The centre of the circle lies in …….. of the circle. (exterior/interior)


(ii) A point, where distance from the centre of a circle is greater than its radius lies in ………. of the circle. (exterior/interior)


(iii) The longest chord of a circle is a …….. of the circle.


(iv) An arc is a …………… when its ends are the ends of a diameter.


(v) A circle divides the plane, on which it lies, in ………….. parts.

 1

Write True/False in the following and give the reason of your answer if possible.

(i) AB and CD are chords of measure 3 cm and 4 cm respectively of a circle by which the angles subtended at the centre are respectively 70° and 50°.


(ii) Chords of a circle whose lengths are 10 cm and 8 cm are initiated at distances 8 cm and 5 cm respectively from the centre.


(iii) Out of the two chords AB and CD of a circle each is at a distance of 4 cm from the centre. Then AB = CD.


(iv) Congruent circles with centres O and O’ intersect at two points A and B. Then ∠AOB = ∠AO’B.


(v) A circle can be drawn through three collinear points.


(vi) A circle of radius 4 cm can be drawn through two points A and B of AB = 8 cm.

 2

If the radius of a circle is 13 cm and length of its one chord is 10 cm, then find the distance of this chord from the centre.

 3

Two chords AB and CD of a circle whose lengths are 6 cm and 12 cm respectively, are parallel to each other and these lie in the same side of the centre of circle. If the distance between AB and CD be 3 cm, then find the radius of the circle.