Two circles share the same centre and have radii 25 cm and 24 cm. A chord of the larger circle just touches the smaller circle. How long is that chord?

At the point of contact the radius 24 of the small circle is perpendicular to the chord, and a perpendicular from the centre bisects a chord. So half the chord is √$(25^2-24^2)=$ √(625 − 576) = √49 = 7 cm, making the whole chord 14 cm. Stopping at 7 cm gives only half the chord.