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

% Ex. No. 35 (Section  5.3 : Internal Similitude Center)

\begin{tikzpicture}[scale=.75,rotate=-30]
 \tkzDefPoint(0,0){O}
 \tkzDefPoint(4,-5){A}
 \tkzDefIntSimilitudeCenter(O,3)(A,1)
 \tkzGetPoint{I}
 \tkzExtSimilitudeCenter(O,3)(A,1)
 \tkzGetPoint{J}
 \tkzDefTangent[from with R= I](O,3 cm)
 \tkzGetPoints{D}{E}
 \tkzDefTangent[from with R= I](A,1 cm)
 \tkzGetPoints{D'}{E'}
 \tkzDefTangent[from  with R= J](O,3 cm)
 \tkzGetPoints{F}{G}
 \tkzDefTangent[from with R= J](A,1 cm)
 \tkzGetPoints{F'}{G'}
 \tkzDrawCircle[R,fill=red!50,opacity=.3](O,3 cm)
 \tkzDrawCircle[R,fill=blue!50,opacity=.3](A,1 cm)
 \tkzDrawSegments[add = .5 and .5,color=red](D,D' E,E')
 \tkzDrawSegments[add= 0 and 0.25,color=blue](J,F J,G)
 \tkzDrawPoints(O,A,I,J,D,E,F,G,D',E',F',G')
 \tkzLabelPoints[font=\scriptsize](O,A,I,J,D,E,F,G,D',E',F',G')
\end{tikzpicture}

\end{document}