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\input{preamble-standalone.ltx}
\begin{document}
% Ex. No. 52 (Section 9.2.2 : Example of \tkzname{homothety} and \tkzname{projection})
\begin{tikzpicture}[scale=1.2]
\tkzDefPoint(0,1){A} \tkzDefPoint(5,3){B} \tkzDefPoint(3,4){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'}
\tkzDefPointBy[projection = onto A--B](a) \tkzGetPoint{k}
\tkzDrawLines[add= 0 and .3](A,k A,C)
\tkzDrawSegments[blue](a',k' a,k)
\tkzDrawPoints(a,a',k,k',A)
\tkzDrawCircles(a',k' a,k)
\tkzLabelPoints(a,a',k,A)
\end{tikzpicture}
\end{document}
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