Data: A line intersects two concentric circles with centre O at A, B, C and D.
To Prove: AB = CD.
Construction: Draw OM⊥AD.
Proof: AD is the chord of bigger circle. OM⊥AD
∴ AM = MD ………(i)
(∵ Perpendicular bisects the chord from centre)
Similarly, BC is the chord of smaller circle. OM⊥BC.
∴ BM = MC ………. (ii)
Subtracting (ii) from (i),
AM – BM = MD – MC
∴ AB = CD.