Question

prove that equal chord of a circle substent equal angles at center

Answer 1

Given : In a circle C(O,r), chord AB = chord CD.

To Prove : ∠AOB = ∠COD. 

Proof : In△AOB and △COD 

AO = CO [radii of same circle] 

BO = DO [radii of same circle]

Chord AB = Chord CD [given]

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

⇒  ∠AOB = ∠COD.   [c.p.c.t.]  

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