CONO-SUR 2012 Problem 6

Consider a triangle $ABC$ with $1 < \frac{AB}{AC} < \frac{3}{2}$ . Let $M$ and $N$ , respectively, be variable points of the sides $AB$ and $AC$ , different from $A$ , such that $\frac{MB}{AC} - \frac{NC}{AB} = 1$ . Show that circumcircle of triangle $AMN$ pass through a fixed point different from $A$ .