Let $ABC$ be an isosceles triangle ($AB = AC$). The points $D$ and $E$ were marked on the ray $AC$ so that $AC = 2AD$ and $AE = 2AC$. Prove that $BC$ is the bisector of the angle $\angle DBE$.
Problem
Source: 2014 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p7
Tags: geometry, isosceles, angle bisector, Ukraine Correspondence