Let $\triangle ABC$ have $AB = 1$ cm, $BC = 2$ cm and $AC = \sqrt{3}$ cm. Points $D$, $E$ and $F$ lie on segments $AB$, $AC$ and $BC$ respectively are such that $AE = BD$ and $BF = AD$. The angle bisector of $\angle BAC$ intersects the circumcircle of $\triangle ADE$ for the second time at $M$ and the angle bisector of $\angle ABC$ intersects the circumcircle of $\triangle BDF$ at $N$. Determine the length of $MN$.