Τετάρτη, 11 Οκτωβρίου 2017

2002 JBMO Shortlist 13

Let ${A_1,A_2, ...,A_{2002}}$ be arbitrary points in the plane. Prove that for every circle of radius ${1}$  and for every rectangle inscribed in this circle, there exist ${3}$  vertices ${M,N, P}$  of the rectangle such that ${MA_1 + MA2 + .. + MA_{2002}+ NA_1 + NA_2 + … + NA_{2002}+ PA_1 + PA_2 + … + PA_{2002 }\ge 6006}$.

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