MathNet 2016-part-03 — 184 problems (EN–VI) Question 183

Let $ABCD$ be a square and $E$ be a point on its diagonal $BD$, different from its midpoint. Denote $H$ and $K$ the orthocenters of the triangles $ABE$, respectively $ADE$. Prove that $\overline{BH} + \overline{DK} = 0$.
Mihaela Berindeanu