Analysis: take the midpoint e of AB and connect OE, DE and OD. According to the fact that the sum of any two sides of a triangle is greater than the third side, it can be known that when the three lines of O, D and E are * * * *, the distance from point D to point O is the largest. Then the length of DE is calculated according to Pythagorean theorem, and the length of OE is calculated according to the fact that the median line on the hypotenuse of right triangle is equal to half of the hypotenuse. Add the two together.

You can get a solution.