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vectors OX\pm OY,. OX\pm OZ, OY \pm OZ, in convex planar set S

Source: IMAR 2012 p1

September 27, 2018

vectorsetvector geometrygeometrycombinatorial geometry

Problem Statement

Let

K

be a convex planar set, symmetric about a point

O

, and let

X, Y , Z

be three points in

K

. Show that

K

contains the head of one of the vectors

\overrightarrow{OX} \pm \overrightarrow{OY} , \overrightarrow{OX} \pm \overrightarrow{OZ}, \overrightarrow{OY} \pm \overrightarrow{OZ}