Question

if the angle suspended by the chords of a circle at the centre are equal than the chords are equal in length- Prove it

Answer 1

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Answer 2

Answer:

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]