Question

In two concentric circle, prove that all chords of the outer circle which touch the inner are of equal length.

Answer 1

Let $AB$ and $CD$ be two chords of the circle which touch the inner circle at $M$ and $N$ respectively.

Then, we have to prove that
$AB=CD$

Proof:

Since $AB$ and $CD$ are tangents to the smaller circle.

$OM=ON=$ Radius of the smaller circle.

Thus, $AB$ and $CD$ are two chords of the larger circle such that they are equidistant from the centre.

Hence, $AB=CD$.