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

Given: Two concentric circles with centre O. AB, CD and EF are the chords of the outer circle.
To prove: AB = CD = EF.
Proof:
OP, OQ and OR are the distances of the chord AB, CD and EF from the centre.
But OP = OR = OQ = radius
Since the chords are at equal distances from the centre they are equal.