Question 178
Let $M$ be the bisector of the base $AB$ of the trapezoid $ABCD$. Inside distance $AC$ lies a point $E$ such that lines $BC$ and $ME$ intersect at point $F$, lines $FD$ and $AB$ intersect at point $G$ and lines $DE$ and $AB$ at point $H$. Prove that $M$ is the bisector of the distance $GH$.