Question

prove that diameter is greatest chord

Answer 1

Since the definition of a diameter is a chord passing through the center of the circle, such an explanation actually reads: "The diameter is the longest chord in a circle because it is a diameter of the circle."

Answer 2

Given:let O be the centre of the circle let AB be the diameter and CD be a chord other than diameter
To Prove: AB>CD
construction: join OC and OD
Proof:OA=OB=OC=OD (radius of circle)
In triangle OCD,
OC+OD>CD
or, OA+OB>CD
Thus,AB>CD