LaTeX-examples/tikz/pentagon-inscribed-circle/pentagon-inscribed-circle.tex

\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
\usepackage{tikz}
\usepackage{tkz-euclide}
\usetkzobj{all}
\usetikzlibrary{shapes, calc, decorations}
\usepackage{amsmath,amssymb}
\usepackage{helvet}
\usepackage[eulergreek]{sansmath}

\begin{document}
\begin{preview}
\begin{tikzpicture}[very thick,font=\sansmath\sffamily]
    \tkzDefPoint(0, 0){CircleCenter}
    \tkzDrawCircle[R](CircleCenter,3cm)

    % Define 5 points on a circle
    \tkzDefPoint( 30:3){BCT}
    \tkzDefPoint( 90:3){CDT}
    \tkzDefPoint(135:3){DET}
    \tkzDefPoint(215:3){EAT}
    \tkzDefPoint(300:3){ABT}

    % Tangents
    \tkzDefLine[perpendicular=through EAT](CircleCenter,EAT)\tkzGetPoint{EAT2}
    \tkzDefLine[perpendicular=through BCT](CircleCenter,BCT)\tkzGetPoint{BCT2}
    \tkzDefLine[perpendicular=through CDT](CircleCenter,CDT)\tkzGetPoint{CDT2}
    \tkzDefLine[perpendicular=through DET](CircleCenter,DET)\tkzGetPoint{DET2}
    \tkzDefLine[perpendicular=through ABT](CircleCenter,ABT)\tkzGetPoint{ABT2}

    % Find the points by intersecting the tangents
    \tkzInterLL(EAT,EAT2)(ABT,ABT2)\tkzGetPoint{A}
    \tkzInterLL(ABT,ABT2)(BCT,BCT2)\tkzGetPoint{B}
    \tkzInterLL(BCT,BCT2)(CDT,CDT2)\tkzGetPoint{C}
    \tkzInterLL(CDT,CDT2)(DET,DET2)\tkzGetPoint{D}
    \tkzInterLL(DET,DET2)(EAT,EAT2)\tkzGetPoint{E}

    % Background
    \tkzDrawPolygon[thick,fill=gray!10](A,B,C,D,E)

    \tkzDrawSegments(CircleCenter,EAT CircleCenter,BCT CircleCenter,CDT CircleCenter,DET CircleCenter,ABT)

    \tkzLabelSegment[left](CircleCenter,EAT){r}
    \tkzLabelSegment[below](CircleCenter,BCT){r}
    \tkzLabelSegment[right](CircleCenter,CDT){r}
    \tkzLabelSegment[right](CircleCenter,DET){r}
    \tkzLabelSegment[right](CircleCenter,ABT){r}


    % Draw points
    \tkzDrawCircle[R,thick,draw=red](CircleCenter,3cm)
    \tkzLabelPoints[below left,font=\sansmath\sffamily](A)
    \tkzLabelPoints[below right,font=\sansmath\sffamily](B)
    \tkzLabelPoints[above right,font=\sansmath\sffamily](C)
    \tkzLabelPoints[above left,font=\sansmath\sffamily](D)
    \tkzLabelPoints[left,font=\sansmath\sffamily](E)


    % % Draw polygon
    \tkzDrawPolygon[very thick](A,B,C,D,E)
\end{tikzpicture}
\end{preview}
\end{document}