Let $h_a$, $h_b$, $h_c$ be the lengths of the altitudes from $A$, $B$, $C$ respectively of a triangle $ABC$. Let $P$ be any point inside the triangle. Prove that
$\frac{PA}{h_b+h_c} + \frac{PB}{h_c+h_a} + \frac{PC}{h_a+h_b} \ge 1$
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