[The horizontal bases of the red and green right triangles above
actually coincide for the most part but I have drawn them slightly 
apart so you can tell which is which. The drawing is approximately
to scale.]

Both the red and the green right triangle have hypotenuse 24,
for that is the given radius of the circle.

The vertical right side of the red right triangle is half of 
the 10 cm chord, or 5 cm.

So the red horizontal base of the red right triangle is
cm.

The vertical right side of the green right triangle is half of 
the 14 cm chord, or 7 cm.

So the green horizontal base of the green right triangle is
cm.

The distance between the two chords is the difference between
the red horizontal base of the red right triangle, and
the green horizontal base of the green right triangle.

Answer: cm.

Edwin