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\begin{tikzpicture}[scale=.5]
 \tkzDefPoint(0,0){O}
 \tkzDefPoint(3,1){I}
 \tkzDefPoint(1,4){J}
 \tkzDefLine[bisector](I,O,J)
   \tkzGetPoint{i}
 \tkzDefLine[bisector out](I,O,J)
   \tkzGetPoint{j}
 \tkzDrawLines[add = 1 and .5,color=red](O,I O,J)
 \tkzDrawLines[add = 1 and .5,color=blue](O,i O,j)
\end{tikzpicture}