The perpendicular from the centre bisects the chord, forming two right triangles. Applying the Baudhāyana–Pythagoras Theorem gives the half-chord as √(r² − d²). Hence, the chord length is 2√(r² − d²).
Explain why the following statement is true: If the perpendicular distance of a chord from the centre is d and the radius is r, then the chord length is 2√(r2-d2 ).
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A perpendicular drawn from the centre to a chord always bisects the chord into two equal parts. Each half forms a right triangle with the radius as the hypotenuse and the perpendicular distance as one side. By applying the Baudhāyana–Pythagoras Theorem, the half-chord equals √(r² − d²). Therefore, the complete chord length is 2√(r² − d²).
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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