\input{preamble-standalone.ltx}
\begin{document}

% Ex. No. 41 (Section  9.2.1 : Example of homothety and projection)

\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}

\end{document}
