Please help me with this task! (11th grade geometry from the exam)

In the triangle ABC, the bisector AE intersects the line drawn through the point B parallel to AC at the point D. BN is the bisector in the triangle ABD. It is known that the circumscribed circle of the triangle NEC passes through the midpoint of DC.

a) Prove that AB = BD
b) Prove that BD is a tangent to a circle circumscribing a triangle EDC.
c) Let BE/EC = 0.8. Find CA/CE.