Question 94
Let $ABC$ be an acute triangle in which $AB \lt AC$. Let $M$ be the midpoint of the side $BC$ and consider $D$ an arbitrary point of the line segment $AM$. Let $E$ be a point of the line segment $BD$ and consider the point $F$ of the line $AB$ such that lines $EF$ and $BC$ are parallel. If the orthocenter, $H$, of the triangle $ABC$ lies at the intersection point of lines $AE$ and $DF$, prove that the angle bisectors of $\angle BAC$ and $\angle BDC$ meet on the line $BC$.