\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}