Question

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Answer 1

(1)

(a) No, all chords are not diameters because diameter is the largest chord of a circle passing through the centre of the circle.

(b) Yes, all diameters are chords but all chords are not diameters because diameter is a chord passing through the centre of a circle.

(c) No, because radii cannot be equal to diameters because radii is the half length of diameter.

(d) No, radii and diameter cannot be equal because radii is half of diameter.

(e) No, because a chord is line attached to two sides of a circle but radius is a line drawn from the centre of a circle to the ends of a circle.

(f) No, the chords and radii can never be equal.

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(2) The figure is attached with the answer..

It is proved with the help of an example.

Given : In a circle C(O,r) , ∠AOB = ∠COD  

To Prove : Chord AB = Chord CD .

Proof : In △AOB and △COD  

AO = CO [radii of same circle]

BO = DO [radii of same circle]

∠AOB = ∠COD  [given]

⇒  △AOB ≅  △COD [by SAS congruence axiom]

⇒   Chord AB = Chord CD [c.p.c.t]