Question

In the following, write  true/false and if possible give reason for your answer.

(i) AB = 3 cm and CD = 4 cm are two chords of a circle. Angles subtended by these chords at center are respectively 70° and 50°.

(ii) Two chords of length 10 cm and 8 cm are at a distance from center 8 cm and 5 cm respectively.

(iii) If two chords AB and CD of a circle are at same distance 4 cm from center then AB = CD.

(iv) Two congruent circles having centers O and O’ intersect each other at two points A and B, then ∠AOB = ∠AO’B.

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

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

Answer 1

(i) False, because longer chord subtends larger angle at the center, where as shorter chord subtends smaller angle at the center.

(ii) False, because larger chords are closer from the center.

(iii) True, because equal chords are equidistant from the center.

(iv) True, because chords of congruent circles, subtend equal angle at the center.

(v) False, because a circle cannot be drawn though three collinear points.

(vi) True, because AB is a diameter.