Question

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

AB = CD

Since AB and CD are tangents to the smaller circle

Therefore, 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.