TR-MO 2018 Problem 4

In a triangle $ABC$ , the bisector of the angle $A$ intersects the excircle that is tangential to side $[BC]$ at two points $D$ and $E$ such that $D\in [AE]$ . Prove that, $$\frac{|AD|}{|AE|}\leq \frac{|BC|^2}{|DE|^2}.$$