Question

prove that equal chords of a circle subtend equal angle at the angle at the centre​

Answer 1

Answer:

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Step-by-step explanation:

Statement : Equal chords of a circle subtend equal angles at the centre.

Given : AB and CD are chords of a circle with centre O, such that AB = CD.

To prove : ∠AOC = ∠COD

Proof :

In ΔAOB and ΔCOD,

AO = CO [radii of same circle]

BO = DO [radii of same circle]

AB = CD [given]

ΔAOB ≅ ΔCOD [SSS]

∠AOB = ∠COD [C. P. C. T]

Hence, Equal chords of a circle subtend equal angles at the centre.

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