\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(3.2,0){B}
    \tkzDefPoint(4.5,0){Z}
    \tkzDefPoint(0.7,3){C}
    \tkzDefBarycentricPoint(A=1,C=2)\tkzGetPoint{X}
    \tkzInterLL(B,C)(X,Z)\tkzGetPoint{Y}

    \tkzDefLine[perpendicular=through A,K=1,/tikz/overlay](Y,Z)\tkzGetPoint{YZA}
    \tkzInterLL(Y,Z)(A,YZA)\tkzGetPoint{YZA}
    \tkzDefLine[perpendicular=through B,K=1,/tikz/overlay](Y,Z)\tkzGetPoint{YZB}
    \tkzInterLL(Y,Z)(B,YZB)\tkzGetPoint{YZB}
    \tkzDefLine[perpendicular=through C,K=1,/tikz/overlay](Y,Z)\tkzGetPoint{YZC}
    \tkzInterLL(Y,Z)(C,YZC)\tkzGetPoint{YZC}

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

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

    % Draw polygon
    \tkzDrawPolygon[thick](A,B,C)

    \tkzDrawSegments[thick,color=blue](A,YZA B,YZB C,YZC)
    \tkzDrawLines[thick](A,Z)
    \tkzDrawLines[thick,color=red](Z,X)

    \tkzLabelSegment[right=-0.1,color=blue](A,YZA){a}
    \tkzLabelSegment[right=-0.01,color=blue](B,YZB){b}
    \tkzLabelSegment[left=-0.1,color=blue](C,YZC){c}

    \tkzDrawPoints[color=black,shape=circle,fill=black,size=2](A,B,C,X,Y,Z,YZA,YZB,YZC)
\end{tikzpicture}
\end{preview}
\end{document}