VMO 1980 — Division A Question 3

Let $P$ lie inside triangle $A_1A_2A_3$. The line $PA_i$ meets the opposite side at $B_i$. Let $C_i$ be the midpoint of $A_iB_i$, and $D_i$ the midpoint of $PB_i$. Compare the areas of triangles $C_1C_2C_3$ and $D_1D_2D_3$.