MathNet 2017-part-02 — 176 problems (EN–VI) Question 176

Let $ABC$ be a triangle with $AB \lt AC$, $H$ its orthocenter, $\Gamma$ its circumcircle, and $d$ the tangent to $\Gamma$ at $A$. Consider the circle with center $B$ passing through $A$. It meets $d$ at $D$ and $(AC)$ at $E$.

Show that $D$, $E$, $H$ are collinear.