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Theorem 3
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 3 Chords of a circle that subtend equal angles at the centre are equal. Given: AB & 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 (Both radius) (Given) (Both radius) (SAS congruency) Thus, by Corresponding parts of Congruent Triangles (CPCT) AB = CD Hence proved
