As can be seen from the figure, since AD is the angular bisector, CD=DE, and then △ACD is congruent △AED.

So AC=AE

The circumference of △DEB is DE+DB+EB = CD+DB+EB = BC+BE = AC+BE = AE+BE = AB = 6.

2

Because △ABC is an isosceles triangle, AD⊥BC,

Then ED is the common side, BD=CD, angle ADB= angle ADC=90.

So △ bed congruence △CED

So EB=EC

Or directly because the angle ADB= angle ADC = 90, EB=EC can be obtained according to Pythagorean theorem.