Question

There are two concentric circles with centre O.AD is a chord of a larger circle intersecting the smaller circle at B and C. Prove that AB=CD...

Answer 1

To prove : AB = CD
Construction : $DrawOM\perp AD.$
Proof : AD is the chord of larger circle
$\therefore AM=DM..\left(i\right)$ [OM bisects the chord]
BC is the chord of smaller circle
$\therefore BM=CM....\left(ii\right)$
[OM bisects the chord]
Substracting (ii) from
(i), we get
$AM-BM=DM-CM\Rightarrow AB=CD$ Proved.