Question 28
In acute triangle $ABC$, denote by $h_a$, $h_b$, $h_c$ the lengths of the altitudes to bases $BC$, $CA$, $AB$, respectively. Point $P$ lies inside the triangle. Prove that
$$
\frac{PA}{h_b + h_c} + \frac{PB}{h_c + h_a} + \frac{PC}{h_a + h_b} \ge 1.
$$
$$
\frac{PA}{h_b + h_c} + \frac{PB}{h_c + h_a} + \frac{PC}{h_a + h_b} \ge 1.
$$