∵AB, AC is the tangent of∵ O,

∴OD⊥AB,OE⊥AC，

∴∠=∠=90 ,

∠∠A = 90°

A quadrilateral is a rectangle,

OD = OE，

A quadrilateral is a square,

O is the midpoint of BC,

∴OD is the center line of △ABC,

AB = AC = 8，

OD = 4，

∴⊙O has a radius of 4.

So the answer is 4.