CR-MO 2010 Problem 1

Consider points $D,E$ and $F$ on sides $BC,AC$ and $AB$ , respectively, of a triangle $ABC$ , such that $AD, BE$ and $CF$ concurr at a point $G$ . The parallel through $G$ to $BC$ cuts $DF$ and $DE$ at $H$ and $I$ , respectively. Show that triangles $AHG$ and $AIG$ have the same areas.