Circles – Exercise 10.2 – (MATHEMATICS) – 9th Class

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Exercise 10.2

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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Sol. Consider, triangles OAB and PQR,

OA = OB = PQ = PR                                    [Radii of congruent circles)

AB = QR                                                        [Given]

∴           ΔOAB ≅  ΔPQR                                             [SSS]

∴    ∠AOB = ∠QPR.                                                  [CPCT]


2. Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

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Sol. Consider, triangles OAB and PQR,

OA = OB = PQ = QR                                                [Radii of congruent circles]


∠AOB = ∠QPR                                                           [Given]

∴   ΔAOB ≅  ΔQPR                                                  [SAS]

⇒            AB  =  QR                                                  [ CPCT]


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