MathNet 2017-part-05 — 176 problems (EN–VI) Question 85

Let $ABC$ be a triangle, with $m(\angle BAC) = 90^\circ$ and $AB = 2AC$. On the ray $CA$ we consider the point $D$ such that $CD = 3CA$. Let $E \in BC$ such that $DE = DB$. Show that $AE \perp BC$.

Adrian Bud