Question

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

Answer 1

Consider two concentric circles with centres at O. Let AB and CD be two chords of the outer circle which touch the inner circle at the points M and N respectively.

To prove the given question, it is sufficient to prove AB = CD.

For this join OM, ON, OB and OD.

Let the radius of outer and inner circles be R and r respectively.

AB touches the inner circle at M.

AB is a tangent to the inner circle