SILK-ROAD 2008 Problem 2

In a triangle $ABC$ $A_0$ , $B_0$ and $C_0$ are the midpoints of the sides $BC$ , $CA$ and $AB$ . $A_1$ , $B_1$ , $C_1$ are the midpoints of the broken lines $BAC,CAB,ABC$ .Show that $A_0A_1,B_0B_1,C_0C_1$ are concurrent.