KöMaL 2008 A468

We are given two triangles. Their side lengths are $a$,$b$,$c$ and $A$,$B$,$C$ respectively, the areas are $t$ and $T$, respectively. Prove that -$a^2 A^2$+$a^2 B^2$+$a^2 C^2$+$b^2 A^2$-$b^2 B^2$+$b^2 C^2$+$c^2 A^2$+$c^2 B^2$-$c^2 C^2 \ge$16$tT$.