Question 86
Let $ABCD$ be a parallelogram. The points $E$ and $F$ on the sides $AB$ and $BC$, respectively, are such that $DE$ is the bisector of $\angle ADF$ and $AE + CF = DF$. The line through $C$ and perpendicular to $DE$ meets the side $AD$ at $L$ and the diagonal $BD$ at $H$. Set $N = DE \cap AC$. Prove that:
a) $AE = DL$;
b) $BC = CD$ if $HN \parallel AD$;
c) $ABCD$ is a square if $HN \parallel AD$.
a) $AE = DL$;
b) $BC = CD$ if $HN \parallel AD$;
c) $ABCD$ is a square if $HN \parallel AD$.