Given: l is a line which intersects two concentric circles (i.e., circles with the same centre) with common centre O at A, B, C and D.
To Prove: AB = CD.
Construction: Draw OE ⊥ l
∴ The perpendicular drawn from the centre of a circle to a chord bisects the chord
∴ AE = ED .....(i)
And BE = EC ....(ii)
Subtracting (ii) from (i), we get
AE - BE = ED - EC
⇒ AB = CD