Question

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

Answer 1

as the chords of the outer circle touches the inner circle it means the chords of the outer circle are tangents of the inner circle therefore,the length of the chords of outer circle or the length of the inner circle is equal.
As we have studied that the tangents to a circle are equal in length

Answer 2

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Given

O is the centre of two concentric circles. AB snd CD are two chords of the outer circle which touch the inner circle at M and N respectively.

To prove

AB = CD

Construction

Join OM and ON

Proof

As AB and CD are tangents of the smaller circle,so OM = ON= Radius of the smaller circle

Clearly, AB and CD are also two chords of the outer circle which are equidistant from its centre O. But chords of a circle equidistant from its centre are equal.

Hence, AB = CD