'There is no chord of a circle that is longer than its diameter.' How do you justify this statement?

Consider any chord AB of a circle with centre O and radius $r$.
 In triangle OAB, OA = OB = $r$.

By the triangle inequality,

$AB \leq OA + OB = 2r$.

The equality AB = 2r holds iff O lies on AB, i.e., AB passes through the centre O, which means AB is the diameter.

Hence no chord can be longer than the diameter (2r). The diameter is the longest chord.

Alternate argument: Since, the chord nearest to the centre is the longest; the closest a chord can get to the centre is when it contains the centre (distance = 0), which is the diameter.
Hence, the diameter is the longest possible chord.