let's have 2n dots and 3n straight line in the plane, with n positive integer.
proof that exist at least one point P in the plane such that the sum of the distances of P to the 3n lines is lower that the sum of the distances of P to the 2n points !

I have started with 2 dots two lines, and two dots and three lines, trying to figure out all the possible configurations.
I would like to make the proof by induction, but it is very tricky!