Because AB is the diameter of circle o,

So ACB angle =90 degrees,

Because the CD tangent circle o is at point C,

So angle ACD= angle ABC,

Because AC bisects the angle DAB,

So angle DAC= angle CAE,

Triangle DAC is similar to triangle cable,

Therefore, angle ADC= angle ACB=90 degrees.

(II) The Link Company.

Because CD is tangent to circle o,

So OC is perpendicular to CD and the angle oce is 90 degrees.

Because the angle ADC=90 degrees,

So OC//AD,

So OC/AD=OE/AE

Let the radius of circle o be r, then OC = R and OE = AE-R.

Because ad = 4 and AE = 12,

So R/4=( 12-R)/ 12.

12R=48-4R

R=3 (that is, the radius of circle O is 3)

Because a triangular ADC is similar to a triangular cable,

So AD/AC=AC/AB.

AC^2=AD*AB

=4X6

=24,

Because CD is tangent to circle o,

So CD 2 = ad * df,

Ac 2 = CD 2+AD 2 = CD 2+ 16。

So CD 2+ 16 = 24.

CD^2=8

So AD*DF=8.

DF=2

So AF=AD-DF

=4-2

=2。