KöMaL 2024 B5371

Let point $P$ be chosen inside triangle $ABC$. Let $D$, $E$ and $F$ denote the orthogonal projections of point $P$ onto sides $BC$, $CA$ and $AB$, respectively. Prove that $\frac{PE+PF}{PA}+\frac{PF+PD}{PB}+\frac{PD+PE}{PC}\le 3$.