Question

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

Answer 1

Given: A circle C(O,r) in which AB is a diameter and CD is any other chord.
To Prove: AB > CD

Proof: Clearly, the diameter AB is nearer to the centre than any other chord CD.
We know that, between any two chords of a circle, the one which is nearer to the centre is longer.
i.e., AB > CD
Thus, AB is longer than every other chord.
Hence, a diameter is the longest chord in a circle.