Question 13
Given an acute triangle $ABC$ in which $|AB| \gt |BC| \gt |AC|$. Let $D$ be a point on the segment $BC$, different from $C$, such that $|AC| = |AD|$. Denote by $H$ the orthocentre of the triangle $ABC$ and by $A_1$ and $B_1$ the feet of the altitudes from $A$ and $B$. The lines $A_1B_1$ and $DH$ intersect at the point $E$. Prove that the points $B$, $D$, $B_1$ and $E$ are concyclic.