Question 4
$ABC$ is right-angled at $A$. Bx bisects angle $B$; $D$ is the perpendicular projection of $C$ onto Bx. $M$ is the midpoint of $AC$, and $DM$ meets $BC$ at $N$. Prove $DAC$ is isosceles, $N$ is the midpoint of $BC$, and find $B$ when $BD = AC$.