Let O be the centre of the two concentric circles and OM the perpendicular from O to the line l. AD is the chord of the larger circle and BC, the chord of the smaller circle.
Since, perpendicular from the centre to a chord bisects the chord, therefore,
AM = MD ...(i)
and BM = MC ...(ii)
(i) and (ii) gives, AM – BM = MD – MC
⇒ AB = CD.