Different points $A$ and $D$ are on the same side of the line $BC$, with $|AB| = | BC|= |CD|$ and lines $AD$ and $BC$ are perpendicular. Let $E$ be the intersection point of lines $AD$ and $BC$. Prove that $||BE| - |CE|| < |AD| \sqrt3$
Problem
Source: Czech-Polish-Slovak Junior Match 2015, Team p3 CPSJ
Tags: geometry, geometric inequality, equal segments, perpendicular