2013 Nantong Rugao second model math junior high school

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

∵ OD≤OE+DE,

∴When O, D, E three points *** line, the distance from the point D to the point O is the largest,

at this time, ∵ AB=2, BC=1,

∴OE=AE=12AB=1,

DE= AD2 + AE2 = (1?+1?) = 2 under the root,

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