Question 14
$E$ is a point on the side $BC$ and $F$ is a point on the side $CD$ of a square $ABCD$ such that the perimeter of triangle $CEF$ is equal to half the perimeter of $ABCD$. $G$ is the point on $AE$ such that $FG$ is perpendicular to $AE$, and $H$ is the point on $FG$ such that $AH=EF$. Prove that $AH$ is perpendicular to $EF$.
