OIM 1992 Problem 6

In a triangle $ABC$ , points $A_{1}$ and $A_{2}$ are chosen in the prolongations beyond $A$ of segments $AB$ and $AC$ , such that $AA_{1}=AA_{2}=BC$ . Define analogously points $B_{1}$ , $B_{2}$ , $C_{1}$ , $C_{2}$ . If $[ABC]$ denotes the area of triangle $ABC$ , show that $[A_{1}A_{2}B_{1}B_{2}C_{1}C_{2}] \geq 13 [ABC]$ .