Let $D$ be a point on the side $AC$ of triangle $\triangle ABC$ such that $AB=AD=DC$ and let $E$ be a point on the side $BC$ such that $BE=2CE$. Prove that $\angle BDE = 90 ^{\circ}$.
Problem
Source: Kosovo National Olympiad 2025, Grade 8, Problem 4
Tags: geometry, national olympiad, Kosovo