Theorem – Equal chords of a circle subtend equal angles at the center

Equal chords of a circle subtend equal angles at the center.

Given:  Two equal chords AB and CD of a circle with center O. i,e. AB = CD.

To prove: ∠AOB = ∠COD

Proof:  In △AOB and △ COD

OA = OC (Radius of circle)
OB = OD (Radius of circle)
AB = CD  (Given)

Hence, △AOB ≅ △ COD (SSS Congruence rule)

    ∴   ∠AOB = ∠COD (Corresponding parts of congruent triangles)

 Hence proved

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