If the angles subtended by two chords of congruent circles at the corresponding centres are equal, the chords are equal.

Explanation

Given: Two congruent circle `C_1` & `C_2` have equal angle at centres.
To Prove: Chords are equal.
Proof:
Let radius of these two circles are `R`
Now in `ΔABC` and `ΔPQR`
`∠ABC=∠PQR` (Given)
`AB=PQ` (Radius of congruent circles are equal)
`BC=QR`
`ΔABC≅ΔPQR` (`SAS` congruence rule)`∴AC=PR` (By `CPCT`)
Hence Proved.