Theorem 10.2 - Class 9 - If angles subtended by chords at center equal.jpg

  1. Chapter 10 Class 9 Circles
  2. Serial order wise
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Transcript

Theorem 10.2 If the angles subtended by the chords of a circle at the center are equal, then the chords are equal. Given : A circle with center O. AB and CD are chords that subtend equal angles at center i.e. ∠AOB = ∠DOC To Prove : AB = CD Proof : In ΔAOB & ΔDOC OA = OD ∠AOB = ∠DOC OB = OC ∴ ∆AOB ≅ ∆ COD ∴ AB = CD Hence, Proved.

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