\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){A}
    \tkzDefPoint(5.0,0){B}
    \tkzDefPoint(4.0,3){C}

    \tkzLabelPoints[below left,font=\sansmath\sffamily](A)
    \tkzLabelPoints[below right,font=\sansmath\sffamily](B)
    \tkzLabelPoints[above,font=\sansmath\sffamily](C)

    % Draw polygon
    \tkzDrawPolygon[thick,fill=gray!10](A,B,C)

    % Mark angles
    \tkzMarkAngle[arc=l,size=0.6cm,fill=green!30](B,A,C)
    \tkzLabelAngle[pos=0.3](B,A,C){$\alpha$}

    \tkzMarkAngle[arc=l,size=0.6cm,fill=red!30](C,B,A)
    \tkzLabelAngle[pos=0.4](C,B,A){$\beta$}

    \tkzMarkAngle[arc=l,size=0.6cm,fill=blue!30](A,C,B)
    \tkzLabelAngle[pos=0.4](A,C,B){$\gamma$}

    % Label lines
    % \tkzLabelSegment[below](A,B){$c$}
    % \tkzLabelSegment[left](A,C){$b$}
    % \tkzLabelSegment[right](B,C){$a$}

    \tkzDefCircle[in,/tikz/overlay](A,B,C)\tkzGetPoint{I}\tkzGetLength{rIN}
    \tkzDrawCircle[R,color=red](I,\rIN pt)

    \tkzInterLC[R,/tikz/overlay](A,B)(I,\rIN pt)
    \tkzGetSecondPoint{ABq}

    \tkzInterLC[R,/tikz/overlay](B,C)(I,\rIN pt)
    \tkzGetSecondPoint{BCq}

    \tkzInterLC[R,/tikz/overlay](C,A)(I,\rIN pt)
    \tkzGetSecondPoint{CAq}

    % Get bisectors
    \tkzDefLine[bisector,/tikz/overlay](B,A,C) \tkzGetPoint{a}
    \tkzInterLL(A,a)(B,C) \tkzGetPoint{a2}
    \tkzDrawLine[add=0 and 0.2,dashed](A,a2)

    \tkzDefLine[bisector,/tikz/overlay](A,C,B) \tkzGetPoint{c}
    \tkzInterLL(C,c)(A,B) \tkzGetPoint{c2}
    \tkzDrawLine[add=0 and 0.2,dashed](C,c2)

    \tkzDefLine[bisector,/tikz/overlay](C,B,A) \tkzGetPoint{b}
    \tkzInterLL(B,b)(A,C) \tkzGetPoint{b2}
    \tkzDrawLine[add=0 and 0.2,dashed](B,b2)

    % Draw segments
    \tkzDrawSegments(I,ABq I,BCq I,CAq)
    \tkzLabelSegment[right](I,ABq){r}
    \tkzLabelSegment[above](I,BCq){r}
    \tkzLabelSegment[left](I,CAq){r}

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