Marinada '21

[lang=hr] Sada je odlučio spustiti okomice iz točke $P$ na stranice trokuta te je nožišta nazvao $D, E$ i $F$. Vedran si uvijek zadaje nove izazove te ga sada zanima maksimum $PD\cdot PE\cdot PF$ na pet decimala. [/lang] [lang=en] Now he has decided to draw lines through point $P$ which are perpendicular to the sides of the triangle and has named the intersection points $ D, E $ and $ F $. Vedran, who always likes to set himself different challenges, is now interested in the maximum $ PD \cdot PE \cdot PF $ rounded to five decimal places. [/lang]