MathNet 2018-part-01 — 181 problems (EN–VI) Question 130

Let $A_1H_1$, $A_2H_2$, $A_3H_3$ be altitudes and $A_1L_1$, $A_2L_2$, $A_3L_3$ be bisectors of an acute angled triangle $A_1A_2A_3$.
Prove the inequality $S(L_1L_2L_3) \ge S(H_1H_2H_3)$ where $S$ stands for the area of a triangle.