Question 17 - End-of-Chapter Exercises - Chapter 5 Class 9 - I’m Up and Down, and Round and Round (Ganita Manja
Last updated at May 26, 2026 by Teachoo
End-of-Chapter Exercises
Question 1
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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)
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End-of-Chapter Exercises
Transcript
Question 17 In a circle with centre O, chords AB and AC are congruent. Explain why this statement is true: "The centre of the circle lies on the angle bisector of ∠BAC ". Given: A circle with center O. Two equal chords, AB and AC i.e. AB = AC. To prove: Angle bisector of ∠ BAC passes through O Proof: Let’s join OA, OB and OC In ΔOAB and ΔOAC AB = AC OB = OC OA = OA ∴ ΔOAB ≅ ΔOAC Thus, by CPCT ∠OAB = ∠OAC Since the line OA perfectly splits ∠BAC into two equal angles, the center O lies directly on the angle bisector of ∠BAC Hence proved
