$P$ is a point inside a triangle $ABC$ of area $K$ ($K>0$) .The lengths of perpendiculars drawn to the sides $BC$, $CA$, $AB$ of lengths $a,b,c$ are respectively $P_1$, $P_2$, $P_3$. If $\frac{a}{P_1} + \frac{b}{P_2} +\frac{c}{P_3}$ is minimum, then $P$ is which special point of triangle? Also find $P_1,P_2,P_3$.
I thought of using Viviani's theorem but realized that it was for equilateral triangle. I am struggling, how to relate area of triangle with given quantities? Also the condition given does not seems direct.