Question

In two concentric circle prove that all the chord of outer circle which touch the inner circle are equal in length

Answer 1

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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