Question 1
Find the point $P$ inside the triangle $ABC$ for which
$$\frac{BC}{PD}+\frac{CA}{PE}+\frac{AB}{PF}$$
is minimal, where $PD,PE,PF$ are the perpendiculars from $P$ to $BC,CA,AB$ respectively.
$$\frac{BC}{PD}+\frac{CA}{PE}+\frac{AB}{PF}$$
is minimal, where $PD,PE,PF$ are the perpendiculars from $P$ to $BC,CA,AB$ respectively.