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In two concentric circles, prove that …

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

Posted by Ritik Raj 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Let the chord AB and CD of outer circle, touch the inner circle at M and N.

Since,OM and ON are radii of the inner circle through the points of contact M and N of the tangents AB and CD, respectively.
{tex}\therefore OM\bot AB{/tex} and {tex}ON\bot CD{/tex}
AB and CD are tangent of inner circle and OM and ON are radii of inner circle.
Also, OM = ON [ ∵ radii of the inner circle]
Thus, AB and CD are two chords of the outer circle which are equidistant from its centre O .
Hence, AB = CD.
So, in two concentric circles all chords of the outer circle which touch the inner circle are of equal length.

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