Geometry Regents Question from regentsprep.org practice questions?

Notice that angle ACD is congruent to ABD because they both intercept the same arc and that angle CEA is congruent to angle BED since they are vertically congruent angles. By A.A. Similarity, triangle CEA is congruent to triangle BED => AE/ED = CE/EB, so AE= CE*ED/EB. Length CE = ED since E is the midpoint. so AE = ED^2 /EB = 4^2 /2 = 8