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

Explanation

Let two concentric circle with center O

Let two chords PQ and RS of the outer circle touches inner circle at point A and B respectively

`:. `PQ and RS becomes tangents to the inner circle

`OA=OB `(Radius of the inner circle)

Thus, chords of the outer circle PQ and RS are equidistant from the center.

`:. PQ=RS`