Q1 of 63 Page 145

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.

(i) False


We know that longer chords subtend at greater angles and smaller chords at smaller angles.


Here CD (longer chord) is subtending at 50° (smaller angle) while AB (smaller chord) is subtending at 70° (greater angle).


So, it is false.


(ii) False


We know that longer the chord, smaller the distance from centre.


Here, 10 cm chord is at a distance of 8 cm from the center, hence it is not possible that 8 cm chord is at a distance of 5 cm from the center.


(iii) True


We know that if two chords are at equal distance from the centre, they are equal.


Here, chords AB and CD are at equal distance of 4 cm from the centre.


∴ AB = CD


Hence, it is true.


(iv) True



We know that equal chords of congruent circles subtend equal angles at the corresponding centres.


If we take AB as chord, and as radius of both circle are equal


⇒ ∠AOB = ∠AO’B


So, it is true.


(v) False


A circle passing through two collinear points cannot pass through the third point.


Hence, it is false.


(vi) True


Given radius = 4 cm


We know that diameter is twice the radius.


When a circle is drawn through two points A and B, diameter will be AB = 8 cm.


Taking a compass, from the centre O and OA or OB as radius, we join A to B and B to A.


So, the circle can be drawn through A and B.


∴ It is true.


More from this chapter

All 63 →
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.

 2

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.

 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.