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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