Since AB and AC are congruent chords, they are equidistant from O. In triangles AOB and AOC, OA is common and OB = OC. Hence, the triangles are congruent, giving ∠BAO = ∠OAC. Therefore, AO bisects ∠BAC.
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”.
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Let AB and AC be congruent chords of a circle with centre O. Equal chords are at equal distances from the centre. Therefore, the perpendicular distances from O to AB and AC are equal. Alternatively, in triangles AOB and AOC, OA is common, OB = OC because they are radii andAB = AC because the chords are congruent. Thus, the triangles are congruent. Hence, ∠BAO = ∠OAC. Therefore, AO bisects ∠BAC.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 5 I’m Up and Down and Round and Round (2026-27):
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