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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. \angleQPR=\angleYXZ

Proof : 

In $\triangle XYZ$ and $\triangle PQR$,

$QR = YZ$ (Given)

$PQ = XY$ (Radii of congruent circle)

$PR = XZ$ (Radii of congruent circle)

Thus,  $\triangle PQR \cong \triangle X Y Z$ (By SSS rule)

$\angle Q P R=\angle \mathrm{YXZ}$ (CPCT)

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seema garhwal

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