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\begin{tikzpicture}[scale=.75,
showbi/.style={bisector,size=2,gap=3}]
\tkzSetUpCompass[color=blue,line width=.3 pt]
\tkzDefPoints{0/1/A, 8/3/B, 3/6/C}
\tkzDrawPolygon(A,B,C)
\tkzDefLine[bisector](B,A,C) \tkzGetPoint{a}
\tkzDefLine[bisector](C,B,A) \tkzGetPoint{b}
\tkzShowLine[showbi](B,A,C)
\tkzShowLine[showbi](C,B,A)
\tkzInterLL(A,a)(B,b) \tkzGetPoint{I}
\tkzDefPointBy[projection= onto A--B](I)
\tkzGetPoint{H}
\tkzDrawCircle[radius,color=gray](I,H)
\tkzDrawSegments[color=gray!50](I,H)
\tkzDrawLines[add=0 and -.2,color=blue!50 ](A,a B,b)
\tkzShowBB
\end{tikzpicture}
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