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.