MathNet 2023-part-05 — 191 problems (EN–VI) Question 24

The triangle $ABC$ has $\angle BAC = 90^\circ$ and $\angle ACB = 54^\circ$. Take the bisector $BD$ ($D \in AC$) of the angle $ABC$ and the point $E$ on the segment $BD$ so that $DE = DC$. Prove that $BE = 2 \cdot AD$.