**Given :** A line AD intersects two concentric circles at A, B, C and D, where O is the centre of these circles.

**To prove :** AB = CD

**Construction :** Draw OM ⊥ AD.

**Proof : **AD is the chord of larger circle.

∴ AM = DM ..(i) [OM bisects the chord]

BC is the chord of smaller circle

∴ BM = CM ..(ii) [OM bisects the chord]

Subtracting (ii) from (i), we get

AM – BM = DM – CM

⇒ AB = CD **Proved.**