Sa se arate ca...

[Marius Mainea]

Sa se arate ca in orice triunghi ascutitunghic ABC are loc inegalitatea:

\( \frac{a+c}{\cos B}+\frac{b+a}{\cos C}+\frac{c+b}{\cos A} \geq 4(a+b+c) \)

Lucian Petrescu GM 2 / 2008

[Marius Mainea]

Folosim CBS.

\( LHS\geq\frac{(2a+2b+2c)^2}{(a+c)\cos B+(b+a)\cos C+(c+b)\cos A}=4(a+b+c) \) deoarece

\( b\cos C+c\cos B=a \) si analoagele.