If a line intersects two concentric circles (circles with the same centre) with centre $O$ at $A, B, C$ and $D$,prove that $AB = CD$.

(N/A) We have two circles with the common centre $O$.
$A$ line $\ell$ intersects the outer circle at $A$ and $D$ and the inner circle at $B$ and $C$. To prove that $AB = CD$,let us draw $OM \perp \ell$.
For the outer circle,
$\because OM \perp \ell$,and the perpendicular from the centre to a chord bisects the chord,
$\therefore AM = MD$ --- $(1)$
For the inner circle,
$\because OM \perp \ell$,
$\therefore BM = MC$ --- $(2)$
Subtracting $(2)$ from $(1)$,we have:
$AM - BM = MD - MC$
$AB = CD$
Hence,it is proved.