Question 122
Let $ABCD$ be a quadrilateral whose diagonals are not perpendicular and whose sides $AB$ and $CD$ are not parallel. Let $O$ be the intersection of its diagonals. Denote with $H_1$ and $H_2$ the orthocenters of triangles $AOB$ and $COD$, respectively. If $M$ and $N$ are the midpoints of the segment lines $[AB]$ and $[CD]$, respectively, prove that the lines $H_1H_2$ and $MN$ are parallel if and only if $AC = BD$.
Flavian Georgescu
Flavian Georgescu