VTMO 2015 — Grade 9 — final Question 4

$ABCD$ is a square with circle centered at A of radius $AB$. $M$ lies on $BC$; its non-side tangent meets $CD$ at $N$. $a$)If $MB = MC$, find $NC : ND$. $b$)Show the circumcenter of $AMN$ lies on a fixed line.