The diameter passes through the centre and is the longest chord of a circle. Any other chord lies away from the centre and is therefore shorter than the diameter. Hence, no chord is longer.
There is no chord of a circle that is longer than its diameter. How do you justify this statement?
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Let the radius of the circle be r. The diameter has length 2r and passes through the centre. For any other chord, the perpendicular from the centre bisects the chord. If its distance from the centre is d, then half the chord is less than r whenever d is greater than zero. Thus, its complete length is less than 2r. Therefore, the diameter is the longest chord, and no chord can be longer than it.
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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