Because DE is tangent and OD is perpendicular to DE, that is, the angle o DE equals 90 degrees, so the angle ADO+ angle CDE equals 90 degrees.

And because angle A= angle ADO, and in the right triangle ABC, angle A+ angle C=90 degrees,

So angle C= angle EDO, that is, DE=EC.

From the tangent length theorem, BE=DE.

Because AB is the diameter, the triangle BDC is a right triangle.

So DE= 1/2BC

(2) Because DE=2 and BC=4,

Because tanC, BD and CD can be found in BD and CD of Rt triangle.

According to photography theorem, BD 2 = ad * CD,

Therefore, AD= 10/3.