Given an isosceles triangle ABC with AB = AC, D is a point on AB such
that AD: DB = 3:1, E is a point on side AC, and when DE and BC
are extended, they meet at a point F, such that DE: EF = 1:3.
(a) Find the ratio AD: AE.
(b) If ABDF is also isosceles, find the ratio DE : BC.