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Theorem 9.8 - Chapter 9 Class 9 Circles
Last updated at May 29, 2023 by Teachoo
Theorems
Theorem 9.1
Theorem 9.2 Important
Theorem 9.3 Important
Theorem 9.4
Theorem 9.5 Important
Theorem 9.6
Theorem 9.7 Important
Theorem 9.8 You are here
Theorem 9.9 Important
Theorem 9.10
Theorem 9.11 Important
Angle in a semicircle is a right angle Important
Only 1 circle passing through 3 non-collinear points Deleted for CBSE Board 2024 Exams
Transcript
Theorem 9.9 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. To Prove : ∠PAQ = ∠PBQ Proof : Chord PQ subtends ∠ POQ at the center From Theorem 9.8: Angle subtended by an arc at the centre is double the angle subtended by it at any other point on circle ∴ ∠ POQ = 2∠PAQ ∠POQ = 2∠PBQ From (1) and (2) 2∠PBQ = 2∠PAQ ∠ PBQ = ∠PAQ Hence, Proved.
