If two arcs of a circle (or of congruent circles) are congruent, then corresponding chords are equal.

Explanation

Let AXB and CYD are arcs of circle whose centre and radus are O and r units, respectively.
So, OA=OB=OC=OD=r …..(i)
`:' "arc "AXB cong"arc "CYD`
` :. angle AOB=angleCOD `
[congruent arcs of a circle subtend equal angles at the centre]
In `DeltaAOB abd DeltaCOD`,
AO=CO [form Eq. (i)]
BO=DO [from Eq.(i)]
`angle AOB=angleCOD` [from Eq. (ii)]
`:.Delta AOB cong Delta COD`[by SAS songruence rule]
`rArr AB=CD` [by COCT]
`rArr (AB)/(CD)=1`
the ratio of AB and CD is `1 : 1`.