Chapter 10 Circles Exercise 10.2
Question 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.Answer:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3CEChpMN9coKBpllqX1pabJpfQ6unSNGnwsgBuIP_-J7hd5RwVVYdecS-IeHRHsEM-MRCHQY_x6Ql4NdJoAqDOUA44qbiR5HvWPOpK0lHROwaCFtVnfcCwyuwKqI7Q32XX1W1CstbakaD/s16000/EXERCISE+10.2.png)
OA = OC (Radii of the circle)
OB = OD (Radii of the circle)
AB = CD (Given)
Therefore, ∆ AOB ≅ ∆ COD (SSS rule). By CPCT, ∠AOB = ∠COD
Question 2: Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.
Answer:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKUqlwv2tu9kOeOq-dJeUdEW6e0P0ZVAZS7cMlTI8RYjyPWEkm88Z1QVc5LqiVCjQ8HWLXDjmOPZe9MkneP7r8JKLIgVmOSRgqm6EKyk2cNI2jFQW_dRwkhLWbovxTx6MTs8FgJpDK16vp/s16000/EXERCISE+10.2+%25281%2529.png)
OA = OC (Radii of the circle)
∠AOB = ∠COD (Given)
OB = OD (Radii of the circle)
Therefore, ∆ AOB ≅ ∆ COD (SAS rule). By CPCT, AB = DC.
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