\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){B}
    \tkzDefPoint(0.5,3){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){$a$}

    \tkzDefLine[orthogonal=through A,/tikz/overlay](B,C) \tkzGetPoint{helper}
    \tkzInterLL(B,C)(A,helper) \tkzGetPoint{La}
    \tkzDrawSegments[red](A,La)

    \tkzDefLine[orthogonal=through B,/tikz/overlay](A,C) \tkzGetPoint{helper}
    \tkzInterLL(A,C)(B,helper) \tkzGetPoint{Lb}
    \tkzDrawSegments[red](B,Lb)

    \tkzDefLine[orthogonal=through C,/tikz/overlay](A,B) \tkzGetPoint{helper}
    \tkzInterLL(A,B)(C,helper) \tkzGetPoint{Lc}
    \tkzDrawSegments[red](C,Lc)

    % next level
    \tkzDefLine[orthogonal=through La,/tikz/overlay](A,C) \tkzGetPoint{helper}
    \tkzInterLL(A,C)(La,helper) \tkzGetPoint{La1}
    \tkzDrawSegments[blue](La,La1)
    \tkzDefLine[orthogonal=through La,/tikz/overlay](A,B) \tkzGetPoint{helper}
    \tkzInterLL(A,B)(La,helper) \tkzGetPoint{La2}
    \tkzDrawSegments[blue](La,La2)

    \tkzDefLine[orthogonal=through Lb,/tikz/overlay](B,C) \tkzGetPoint{helper}
    \tkzInterLL(B,C)(Lb,helper) \tkzGetPoint{Lb1}
    \tkzDrawSegments[blue](Lb,Lb1)
    \tkzDefLine[orthogonal=through Lb,/tikz/overlay](B,A) \tkzGetPoint{helper}
    \tkzInterLL(B,A)(Lb,helper) \tkzGetPoint{Lb2}
    \tkzDrawSegments[blue](Lb,Lb2)

    \tkzDefLine[orthogonal=through Lc,/tikz/overlay](A,C) \tkzGetPoint{helper}
    \tkzInterLL(A,C)(Lc,helper) \tkzGetPoint{Lc1}
    \tkzDrawSegments[blue](Lc,Lc1)
    \tkzDefLine[orthogonal=through Lc,/tikz/overlay](B,C) \tkzGetPoint{helper}
    \tkzInterLL(B,C)(Lc,helper) \tkzGetPoint{Lc2}
    \tkzDrawSegments[blue](Lc,Lc2)

    \tkzCircumCenter(La1,La2,Lb1)\tkzGetPoint{T}
    \tkzDrawCircle(T,La1)

    \tkzDrawPoints[size=1, fill=black](La1, La2, Lb1, Lb2, Lc1, Lc2, T)
    \tkzLabelPoints[right](T)

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