Mathematics
Answer
Given: AB and CD are two equal chords of a circle with center O.
To prove: ∠AOB = ∠COD
Construction: Join OA, OB, OC, OD.
Proof: In Δ AOB and Δ COD,
OA = OC (Radii of a circle)
OB = OD (Radii of a circle)
AB = CD (Given)
By SSS congruency criterion,
Δ AOB ≅ Δ COD
Using corresponding parts of congruent triangles,
∠AOB = ∠COD
Hence, equal chords of a circle subtend equal angles at the centre.
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