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\begin{tikzpicture}[scale=1.25]
\tkzInit \tkzClip
\tkzDefPoint(0,1){A} \tkzDefPoint(6,3){B} \tkzDefPoint(3,6){C}
\tkzDrawLines[add= 0 and .3](A,B A,C)
\tkzDefLine[bisector](B,A,C) \tkzGetPoint{a}
\tkzDrawLine[add=0 and 0,color=magenta!50 ](A,a)
\tkzDefPointBy[homothety=center A ratio .5](a) \tkzGetPoint{a'}
\tkzDefPointBy[projection = onto A--B](a') \tkzGetPoint{k}
\tkzDrawSegment[blue](a',k)
\tkzDrawPoints(a,a',k,A)
\tkzDrawCircle(a',k)
\tkzLabelPoints(a,a',k,A)
\end{tikzpicture}
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