Question

Prove that equal chords of a circle subtend equal angles at the centre.​

Answer 1

❇️ Question :-

Prove that equal chords of a circle subtend equal angles at the centre.

❇️ Solution :-

✍️ Given :-

A circle with centre O, AB and AC are equal chords of circle.

• AB = AC

✍️ To prove :-

We have to prove that <AOB = <DOC

✍️ Proof :-

In ∆AOB and ∆AOC,

AO = OD [Radii]

AB = CD [Given]

OB=OC [Radii]

✍️ Therefore, by SSS rule, ∆AOB=~∆AOC.

<AOB = <DOC [CPCT]

✍️Hence, proved !!

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All done :)