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Kürschák Math Competition
2011 Kurschak Competition
3
3
Part of
2011 Kurschak Competition
Problems
(1)
Distance to lines and points
Source: Kürschák competition 2011 P3
3/2/2020
Given
2
n
2n
2
n
points and
3
n
3n
3
n
lines on the plane. Prove that there is a point
P
P
P
on the plane such that the sum of the distances of
P
P
P
to the
3
n
3n
3
n
lines is less than the sum of the distances of
P
P
P
to the
2
n
2n
2
n
points.
combinatorial geometry
inequalities