MathNet 2024-part-01 — 168 problems (EN–VI) Question 98

Given is a triangle $ABC$ and two points $D \in AC$, $E \in BD$ such that $\angle DAE = \angle AED = \angle ABC$. Show that $BE = 2CD$ if and only if $\angle ACB = 90^\circ$.
(Nikolay Nikolov)