In a triangle  , points  and  are chosen in the prolongations beyond  of segments  and  , such that  . Define analogously points  ,  ,  ,  . If ![[ABC]](http://data.artofproblemsolving.com/images/latex/8/b/7/8b78d271c3d197e48980793383e67d5fd4a27dfc.gif "[ABC]") denotes the area of triangle , show that ![[A_{1}A_{2}B_{1}B_{2}C_{1}C_{2}] \geq 13 [ABC]](http://data.artofproblemsolving.com/images/latex/4/4/f/44f28217ae8fb15af1ea2e81014570041f9c7c99.gif "[A_{1}A_{2}B_{1}B_{2}C_{1}C_{2}] \geq 13 [ABC]") .
Solución. |
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In a triangle , points and are chosen in the prolongations beyond of segments and , such that . Define analogously points , , , . If denotes the area of triangle , show that .
Solución. |
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