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Angles in the same segment are equal
Last updated at May 26, 2026 by Teachoo
Class 9
Chapter 5 Class 9 - I’m Up and Down, and Round and Round (Ganita Manja
- Definitions
- Symmetries of Circle
- Number of Circles
- Exercise Set 5.1
- Think, Draw and Infer (Page 98)
- Angle Subtended by Chords
- Exercise Set 5.2
- Mid-points and Perpendicular Bisectors of Chords
- Exercise Set 5.3
- Distance of Chords from the Centre
- Exercise Set 5.4
- Distance of unequal chords from center
- Exercise Set 5.5
- Angle subtended by an arc
- Exercise Set 5.6
- Concyclicity of Points and Cyclic Quadrilateral
-
Theorems (and their Proofs)
- End-of-Chapter Exercises
Transcript
Theorem 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: 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
