In this figure, because 0C=OC=3, BC=2, and the angle C is 90, AB = "four times the root of 2" and OD=2.

According to the fact that the center line of the hypotenuse of a right triangle is half of the hypotenuse, the length of BD is "double radical" (words are used to replace it if it can't be typed), so OD+BD = double radical, and because the distance of OB is required to be the largest, the OB value is the largest when OB=OD+BD.

So choose one