Question 3
Let $ABC$ be an acute triangle with altitudes $AD$, $BE$ and $CF$ (with $D$ on $BC$, $E$ on $AC$ and $F$ on $AB$). Let $M$ be the midpoint of segment $BC$. The circumcircle of triangle $AEF$ meets line $AM$ at $A$ and at $X$. Line $AM$ meets line $CF$ at $Y$. Let $Z$ be the intersection point of lines $AD$ and $BX$.
Prove that lines $YZ$ and $BC$ are parallel.
Prove that lines $YZ$ and $BC$ are parallel.