MathNet 2016-part-03 — 184 problems (EN–VI) Question 139

Let $ABCD$ be a square and let $E$ be a point on the diagonal $BD$, different from its midpoint. Let $H$ and $K$ be the orthocenters of triangles $ABE$ and $ADE$, respectively. Show that $\overline{BH} + \overline{DK} = 0$ (as vectors).