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

Explanation

To prove: `AB>CD`
Construction: Join `OC` and `OD`.
Proof: 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.
`OA=OB=OC=OD` (Radius of the circle)
Now In `triangleOCD`,
`OC+OD>CD`
`OA>OB>CD`
`=>AB>CD
`therefore AC>CD`
Hence proved.