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Theorem 10.9 - Class 9th - Angles in the same segment of a circle are equal - Angle subtended by arc at the centre

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  1. Chapter 10 Class 9 Circles
  2. Serial order wise
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Theorem 10.9 Angles in the same segment of a circle are equal. Given : A circle with center at O. Points P & Q on this circle subtends angles ∠ PAQ and ∠ PBQ at points A and B respectively. And chord PQ subtends ∠ POQ at the center To Prove : ∠PAQ = 2∠PBQ Proof : From Theorem 10.8: Angle subtended by an are an centre is double the angle subtended by it at any other point on circle ∴ ∠ POQ = 2∠PAQ Similarly, ∠POQ = 2∠PBQ From (1) and (2) 2∠PBQ = 2∠PAQ ∠ PBQ = ∠PAQ Hence, Proved.

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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