Let point $P$ be inside of $\Delta ABC$, and 3 lines through $\{A,P\ \},\{B,P\ \}$, and $\{C,P\ \} $ intersect

$\Delta ABC $ at $A_1, B_1, C_1$ respectively. Let $A_2, B_2, C_2$ be middle points of $\overline{AA}_1,\ \overline{BB}_1$ and $\overline{CC}_1$.

Show that $\ |\Delta A_1 B_1 C_1|= 4|\Delta A_2 B_2 C_2|$