Two parallel chords of a circle of radius 13 cm measure 10 cm and 24 cm, and both lie on the same side of the centre. How far apart are the two chords?

The perpendicular from the centre bisects each chord. For the 10 cm chord the distance is √$(13^2-5^2)=$ √144 = 12 cm; for the 24 cm chord it is √$(13^2-12^2)=$ √25 = 5 cm. Since both chords are on the same side of the centre, the gap between them is 12 − 5 = 7 cm. If they were on opposite sides the answer would be 12 + 5 = 17 cm.