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.

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.

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.

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.

In figure, two equal chords AB and CD intersect each other at E. Prove that arc DA = arc CB.