It is discussed in two cases: ① The chords AB and CD are on the same side of the center of the circle; ② The chords AB and CD are on different sides of the center of the circle; Make radius and chord center distance, and solve it by Pythagorean theorem and vertical diameter theorem. Be careful not to miss the solution.

Solution: ① When the chords AB and CD are on the same side of the center of the circle, as shown in figure 1,

AB = 24cm，CD= 10cm，

∴AE= 12cm,CF=5cm，

∫OA = OC = 13cm，

∴EO=5cm,OF= 12cm，

∴ef= 12-5=7cm；

② When the chords AB and CD are on different sides of the center of the circle, as shown in Figure 2,

AB = 24cm，CD= 10cm，

∴AE= 12cm,CF=5cm，

∫OA = OC = 13cm，

∴EO=5cm,OF= 12cm，

∴EF=OF+OE= 17cm.

∴ The distance between AB and CD is 7cm or17cm. ..