Two circles of radii 12 cm and 13 cm are concentric. The length of the chord of the larger circle which touches the smaller circle is:

The chord of the larger circle (radius 13) that is tangent to the smaller circle (radius 12) has its midpoint at distance 12 from the centre. Half-length = √(13²−12²) = √(169−144) = √25 = 5 cm. Full chord = 10 cm.