Recall that two circles are congruent if they | vedclass

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(N/A) Consider two congruent circles with centres $O$ and $O'$. Let $AB$ and $CD$ be equal chords of these circles respectively,such that $AB = CD$.We

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(N/A) Consider two congruent circles with centres $O$ and $O'$. Let $AB$ and $CD$ be equal chords of these circles respectively,such that $AB = CD$.
We need to prove that $\angle AOB = \angle CO'D$.
In $\Delta AOB$ and $\Delta CO'D$:
$AO = CO'$ (Radii of congruent circles are equal)
$BO = DO'$ (Radii of congruent circles are equal)
$AB = CD$ (Given)
By the $SSS$ (Side-Side-Side) congruence criterion,$\Delta AOB \cong \Delta CO'D$.
Since congruent triangles have equal corresponding parts,we have:
$\angle AOB = \angle CO'D$.
Hence,equal chords of congruent circles subtend equal angles at their centres.

Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

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