Because BD=DC, D is the midpoint of BC.

So DE is the center line of △ABC.

∴DE∥AC and DE = 1/2AC②

Ad ⊥ AC，∠ bad = 30 ∴∠ BAC = ∠ bed = 120。

∴∠AED=60，∠ADE=90，DE= 1/2AE③

AC= 1/2AB is known from ① ② ③.