(2) In the right triangle ABC, calculate its three sides according to the concept of acute trigonometric function and Pythagorean theorem, and then calculate according to similar triangles's judgment and properties.
Solution: (1) Proof: Connect BD,
∫AB is the diameter, ∠ ABC = 90,
∴BC is the tangent of⊙ O, and∠ ∠BDC = 90°.
And DE is the tangent of ⊙O,
∴DE=BE.
∴∠EBD=∠EDB.
And < DCE+< EBD = < CDE+< EDB = 90,
∴∠DCE=∠CDE,
∴DE=CE.
So DE= BC ..
(2) From (1), BC = 2DE = 4.
In Rt△ABC, AB=BCtanC=4× radical number 5/2 =2 radical number 5,
So AC= 6 (Pythagorean theorem).
∠∠ADB =∠ABC = 90,∠A=∠A,
∴ABD∽△ACB.
∴AD/AB=AB/AC
∴AD/ root number 5= root number 5/6
The solution is AD= 10/3.