Consider a fixed point $O$ and $n$ fixed straight lines. Through $O$ a variable line is drawn intersecting the fixed lines in $P_1,P_2,\ldots,P_n$. On this variable line, a point $P$ is taken such that $n/OP=1/OP_1+1/OP_2+\cdots+1/OP_n$. How to find the locus of $P$?
My methods are becoming long.What should be the correct approach?