In two concentric circles, prove that all chords of the outer circleto

1.	In two concentric circles, prove that all chords of the outer circletouch the inner circle, are of equal length.
Answer» Let PQ and RS be the chords of the circle that touch the inner circle at M and N respectively. PQ and RS are the tangents to the inner circle, and OM and ON are the radii of the smaller circle. OM = ON Thus PQ and RS are equidistant from the centre, therefore they are equal. Hence PQ = RS.

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

Answer»

Let PQ and RS be the chords of the circle that touch the inner circle at M and N respectively.

PQ and RS are the tangents to the inner circle, and OM and ON are the radii of the smaller circle.

OM = ON

Thus PQ and RS are equidistant from the centre, therefore they are equal.

Hence PQ = RS.