Consider a variable point inside a given triangle . Let , , be the feet of the perpendiculars from the point to the lines , , , respectively. Find all points which minimize the sum
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Consider a variable point $P$ inside a given triangle $ABC$. Let $D$, $E$, $F$ be the feet of the perpendiculars from the point $P$ to the lines $BC$, $CA$, $AB$, respectively. Find all points $P$ which minimize the sum $${BC\over PD}+{CA\over PE}+{AB\over PF}.$$
Izvor: Međunarodna matematička olimpijada, shortlist 1981
Školjka 
inside a given triangle 
. Let 
, 
, 
be the feet of the perpendiculars from the point 
, 
, 
, respectively. Find all points 