Question 3
$ABC$ is right at A with $AB \lt AC$. $M$ is the midpoint of $BC$; $D$ lies opposite A across $M$. $E , F$ are projections of $B , C$ onto $AD$. Prove $BFD = CEA$. Let $DK$ be perpendicular to $BC$ and $N = DK \cap BE$; prove $AN = NC$ and find $ANC$ when $B = 60 ^{\circ}$.