Locus of points minimizing sums of distances with hexagon
Source: Italian National Olympiad 2007, problem 1
May 13, 2007
geometryinequalitiescircumcircletriangle inequalitygeometry proposed
Problem Statement
It is given a regular hexagon in the plane. Let P be a point of the plane. Define s(P) as the sum of the distances from P to each side of the hexagon, and v(P) as the sum of the distances from P to each vertex.
a) Find the locus of points P that minimize s(P)
b) Find the locus of points P that minimize v(P)