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\title{Bisecting a Segment in the Klein Model
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\author{P. Coulton \thanks{Author, E-mail: prccoulton@eiu.edu}}    % Declares the author's name.
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\date{Department of Mathematics \medbreak Eastern Illinois University
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{\bigbold Abstract}
We show that the segment bisector of any segment  whose extended line is a Euclidean 
distance $a$ below  the origin on the $y$-axis  in the Klein model is obtained by finding  a point the line $y=-1/a$  and constructing the 
lines from this point $Q$ to obtain a "bow-tie" relation.
\medbreak \noindent {\it AMS classification:} 52B05, 52B55
\medbreak \noindent {\it Keywords:} Klein model, segment bisector
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 \noindent
{\bf Section1.}
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\begin{center}
\includegraphics[scale=0.4]{pixs/bisectors}
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Fig. 1.1.  {\it This construction is the basis of the proof.} \hskip2truecm
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\noindent Department of Mathematics
\par \noindent  Eastern Illinois University
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