Question 122
A kite is a quadrilateral whose diagonals are perpendicular. Let kite $ABCD$ be such that $\angle B = \angle D = 90^{\circ}$. Let $M$ and $N$ be the points of tangency of the incircle of $ABCD$ to $AB$ and $BC$ respectively. Let $\omega$ be the circle centered at $C$ and tangent to $AB$ and $AD$. Construct another kite $AB' C' D'$ that is similar to $ABCD$ and whose incircle is $\omega$. Let $N'$ be the point of tangency of $B' C'$ to $\omega$. If $MN' \parallel AC$, then what is the ratio of $AB : BC$?