Question 5
$ABCD$ is a square centered at $O$. $M$ lies inside $AB$; the line through $M$ parallel to $BD$ meets $AC$ at $N$. Let $E = DN \cap CM$ and $F = DN \cap AB$. $a$)Show $\angle DEC$ is constant. $b$)Show $E$ lies on circle $\left(O , OA\right)$. $c$)Maximize $MF$.