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\begin{tikzpicture}[scale=1.5]
 \tkzInit[xmin=0,xmax=4,ymin=0,ymax=3] \tkzClip
 \tkzDefPoint(0,0){A} \tkzDefPoint(4,0){B}
 \tkzDefPoint(1,3){C} \tkzDrawPolygon(A,B,C)
 \tkzSetUpLine[color=purple]
 \tkzDrawLine[bisector](B,C,A)
 \tkzDrawLine[bisector](C,A,B)
 \tkzDrawLine[bisector](A,B,C)
\end{tikzpicture}