Analysis: According to the nature of isosceles triangle, we know that if A is the vertical line of BC and the vertical foot is D, then AD divides BC vertically; According to the vertical diameter theorem, AD must pass through the center o; According to the properties of isosceles right triangle, it is easy to find out the length of BD and AD, and then find out the value of OD. The radius of ⊙O can be found by connecting OB according to Pythagorean theorem. Solution: Let A be AD⊥BC. From the meaning of the question, it can be known that AD must pass through point O and connect OB;

∵△BAC is isosceles Rt△, AD⊥BC,

∴bd=cd=ad=3；

∴od=ad-oa=2；

In Rt△OBD, according to Pythagorean theorem, we get:

OB= root number (square of BD's square CD) = root number 13.

So choose D.