Prove that if the angles subtended by the chords of a circle at the centre are equal, then chords
are equal.
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It means that once two triangles are proven to be congruent, then the three pairs of sides that correspond must be congruent and the three pairs of angles that correspond must be congruent.] Thus, we conclude that if the angles made by the chords of a circle at the centre are equal, then the chords must be equal.
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To Prove: AB=CD
Proof:- In △AOB & △DOC
OA=OD[radius],∠AOB=∠DOC(given)
OB=OC(radius)
∴△AOB≅△COD[SAS congr]
∴AB=CD [By cpct]
Hence proved.
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