MathNet 2023-part-02 — 191 problems (EN–VI) Question 13

Let $ABC$ be a triangle with a right angle at $B$ and $BC \lt BA$. Let $D$ be the point of the segment $[AB]$ such that $BD = BC$. The perpendicular to $(AC)$ through $D$ meets $(AC)$ at $E$. Let $B'$ be the reflection of $B$ in $(CD)$. Show that $(EC)$ is the bisector of the angle $\widehat{BEB'}$.