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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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Let O be the center of the circle ABCD. Let AB be the diameter and CD be a chord other than diameter of the circle.
Prove that : AB>CD
Cons. : JOIN OC and OD
Proof: OA=OB=OC=OD (radius of the same circle)
Now In `triangleOCD`
`OC+OD>CD`
or, `OA+AB>CD`
`therefore` `AB>CD`
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