State and prove that: Theorem 10.2 : If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.
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**Theorem 10.2: If the angles subtended by the chords of a circle at the center are equal, then the chords are equal.**
**Proof:**
1. **Given:** Let \( O \) be the center of the circle, and let \( AB \) and \( CD \) be two chords of the circle such that the angles subtended by these chords at the center \( O \) are equal. That is, \( \angle AOB = \angle COD \).
2. **To Prove:** We need to prove that the chords \( AB \) and \( CD \) are equal, i.e., \( AB = CD \).
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