Prove that equal chords of a circle subtend equal angles at the centre.

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Solution

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] (0.5 marks)
BO = DO [radii of same circle] (0.5 marks)
Chord AB = Chord CD (given]
⇒ ∆AOB = ∆COD (by SSS congruence axiom)
⇒ ∠AOB = ∠COD (CPCT) (1 mark)

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