Problem

Source:

Tags: geometry, Concyclic, orthocenter



Let $ABC$ be an acute triangle such that $AB>BC>AC$. Let $D$ be a point different from $C$ on the segment $BC$, such that $AC=AD$. Let $H$ be the orthocenter of triangle $ABC$ and let $A_1$ and $B_1$ be the intersections of the heights from $A$ and $B$ to the opposite sides, respectively. Let $E$ be the intersection of the lines $A_1B_1$ and $DH$. Prove that $B$, $D$, $B_1$, $E$ are concyclic.