Solution: As shown in the figure, take the midpoint E of AB and connect OE, DE and OD.

∫OD≤OE+DE，

∴ When three straight lines O, D and E form * * *, the distance from point D to point O is the largest.

At this time, AB = 2, BC= 1,

∴OE=AE= 12AB= 1，

DE= AD2+AE2= root number = 1 below? + 1? ) = 2 under the root sign,

∴ The maximum value of OD is: 2+ under the root sign? 1.