1993 OIM Problems/Problem 5
Problem
Let and
be two different points on the plane. Let us denote by
the bisector of the segment
. Let
be a finite subset of the plane, with more than one element satisfying the following properties:
a. If and
are points distinct from
, then
intersects
.
b. If ,
and
are three different segments whose ends are points of
, then no point of
belongs simultaneously to the three lines
,
. and
.
Determine the number of points that can have.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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