# So many lines!

Geometry Level 4

A line $$M$$ passing through a fixed point $$O$$ intersects $$n$$ given straight lines $$\{L_i \}$$ at points $$\{B_i\}$$ respectively. Suppose there is a point $$P$$ on line $$M$$ such that the following equation holds true

$\dfrac{n}{OP} = \sum_{i=1}^n \dfrac{1}{OB_i}$

then what is the locus of all such points $$P$$?

Clarification: All the above points lie in $${\mathbf{R}}^2$$ and $$AB$$ denotes the minimum distance between the points $$A$$ and $$B$$.

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