If the angles subtended by two chords of a circle at the centre are equal, then the lengths of the chords are unequal.
False
Let us consider two chords AB and MN of the circle.
It is given that the angles subtended by these chords at the centre is are equal. Say, ∠AOB=∠MON=x.
Let us join the ends of the chords to the centre O.
Now, consider ΔABO and ΔMNO.
Note that OA = OM = radius of the circle,
OB = ON = radius of the circle
and ∠AOB=∠MON(=x∘)
Therefore by SAS criterion, ΔAOB≅ΔMON.
By CPCT, we have AB = MN.