VMO 1980 Problem 3

P is a point inside the triangle $A_1A_2A_3$. The ray $A_i$P meets the opposite side at $B_i$. $C_i$ is the midpoint of $A_iB_i$ and $D_i$ is the midpoint of $PB_i$. Show that area $C_1C_2C_3$ = area $D_1D_2D_3$.