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Prove that the diameter is the greatest ...

Prove that the diameter is the greatest chord in a circle.

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Given A circle C(O,r) in which AB is a diameter and CD is any other chord.
To Prove `AB gt CD`
Proof. Clearly, the diameter AB is nearer to the centre than any other chord CD.
But, of any two chords of a circle, the one which is nearer to the centre is longer.
`:. AB gt CD`.
Thus, AB is longer than every other chord.
Hence, a diameter is the longest chord in a circle.
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