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# 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.

Q: 1     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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Given: The two circles are congruent if they have the same radii.

To prove: The equal chords of congruent circles subtend equal angles at their centres i.e. $\angle$BAC=$\angle$QPR

Proof :

In $\triangle$ABC and $\triangle$PQR,

BC = QR         (Given)

AB = PQ          (Radii of congruent circle)

AC = PR          (Radii of congruent circle)

Thus,  $\triangle$ABC $\cong$ $\triangle$PQR         (By SSS rule)

$\angle$BAC=$\angle$QPR        (CPCT)

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