IL-GILLIS 2020 Problem 7

Let $P$ be a point inside a triangle $ABC$ , $d_a$ , $d_b$ and $d_c$ be distances from $P$ to the lines $BC$ , $AC$ and $AB$ respectively, $R$ be a radius of the circumcircle and $r$ be a radius of the inscribed circle for $\Delta ABC.$ Prove that: $$\sqrt{d_a}+\sqrt{d_b}+\sqrt{d_c}\leq\sqrt{2R+5r}.$$