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

Sum

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

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Solution

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

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

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