Q1 of 63 Page 139

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.

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


We know that the centre is a fixed point in a circle i.e. interior of the circle.


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


If the point’s distance from centre of circle is equals to its radius, then it lies on the circle.


If the distance is greater than the radius, then it lies in exterior of the circle.


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


A chord that passes through the centre of the circle is the longest chord and therefore it is the diameter.


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



Let AB be the diameter and AXB be the arc.


Here, we can see that AXB is a semicircle.


Thus, an arc is a semicircle when its ends are the ends of a diameter.


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


We know that a circle divides the plane on which it lies into three parts i.e.


1. Interior


2. Circle


3. Exterior


More from this chapter

All 63 →
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.

 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.