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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} \ No newline at end of file