given two concentric circles construct a particular chord

Question

I am stumped by another Euclidea problem - Euclidea problem 9.8:

Given two concentric circles $C_1$ and $C_2$ with radians $r_1$ and $r_2$, with $r_1 < r_2 < 2 r_1 $

Construct the chord $e$ of $C_2$ intersecting $C_2$ at $A$ and $B$, $C_1$ at $D$ and $E$ such that $AD < AE$ and $ AD = DE = EB $

(so the chord is trisected by $C_1$ )

Please only a hint

Answer 1

A hint, you say? Use the chord theorem at $D$.