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Sa se arate ca intr-un triunghi oarecare exista inegalitatea \( \underline {\overline {\left\|\ \frac {a}{r_a}+\frac {b}{r_b}+\frac {c}{r_c}\ge \frac {2p}{2R - r}\ \right\|}} \) .

Se stie ca \( \sum {ar_a}=2p(2R-r) \)

Aplicand CBS \( \sum {\frac{a}{r_a}=\sum {\frac {a^2}{ar_a}}\geq\frac{(a+b+c)^2}{ar_a+br_b+cr_c}=\frac{2p}{2R-r} \)