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.

Answers (1)

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. \angleBAC=\angleQPR

Proof : 

In \triangleABC and \trianglePQR,

     BC = QR         (Given)

    AB = PQ          (Radii of congruent circle)

    AC = PR          (Radii of congruent circle)

Thus,  \triangleABC \cong \trianglePQR         (By SSS rule)

     \angleBAC=\angleQPR        (CPCT)

 

 

 

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