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IMAR Test
2012 IMAR Test
1
1
Part of
2012 IMAR Test
Problems
(1)
vectors OX\pm OY,. OX\pm OZ, OY \pm OZ, in convex planar set S
Source: IMAR 2012 p1
9/27/2018
Let
K
K
K
be a convex planar set, symmetric about a point
O
O
O
, and let
X
,
Y
,
Z
X, Y , Z
X
,
Y
,
Z
be three points in
K
K
K
. Show that
K
K
K
contains the head of one of the vectors
O
X
→
±
O
Y
→
,
O
X
→
±
O
Z
→
,
O
Y
→
±
O
Z
→
\overrightarrow{OX} \pm \overrightarrow{OY} , \overrightarrow{OX} \pm \overrightarrow{OZ}, \overrightarrow{OY} \pm \overrightarrow{OZ}
OX
±
O
Y
,
OX
±
OZ
,
O
Y
±
OZ
.
vector
set
vector geometry
geometry
combinatorial geometry