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

% Ex. No. 172 (Section 20.3.5 : With the option \tkzimp{with nodes})

\begin{tikzpicture}[scale=.5]
 \tkzDefPoints{0/0/a,0/5/B,5/0/C}
 \tkzDefPoint(54:5){F}
 \tkzDrawCircle[color=gray](A,C)
 \tkzInterCC[with nodes](A,A,C)(C,B,F)
 \tkzGetPoints{a}{e}
 \tkzInterCC(A,C)(a,e) \tkzGetFirstPoint{b}
 \tkzInterCC(A,C)(b,a) \tkzGetFirstPoint{c}
 \tkzInterCC(A,C)(c,b) \tkzGetFirstPoint{d}
 \tkzDrawPoints(a,b,c,d,e)
 \tkzDrawPolygon[color=red](a,b,c,d,e)
 \foreach \vertex/\num in {a/36,b/108,c/180,
                          d/252,e/324}{%
 \tkzDrawPoint(\vertex)
 \tkzLabelPoint[label=\num:$\vertex$](\vertex){}
 \tkzDrawSegment[color=gray,style=dashed](A,\vertex)
 }
\end{tikzpicture}

\end{document}