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+\documentclass{article}
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+\usepackage[pdftex,active,tightpage]{preview}
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+\setlength\PreviewBorder{2mm}
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+\usepackage{tikz}
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+\usepackage{tkz-euclide}
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+\usetkzobj{all}
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+\usetikzlibrary{shapes, calc, decorations}
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+\usepackage{amsmath,amssymb}
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+\usepackage{helvet}
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+\usepackage[eulergreek]{sansmath}
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+
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+\begin{document}
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+\begin{preview}
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+\begin{tikzpicture}[very thick,font=\sansmath\sffamily]
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+ \tkzDefPoint(0,0){A}
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+ \tkzDefPoint(3.2,0){B}
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+ \tkzDefPoint(4.5,0){Z}
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+ \tkzDefPoint(0.7,3){C}
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+ \tkzDefBarycentricPoint(A=1,C=2)\tkzGetPoint{X}
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+ \tkzInterLL(B,C)(X,Z)\tkzGetPoint{Y}
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+
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+ \tkzDefLine[perpendicular=through A,K=1,/tikz/overlay](Y,Z)\tkzGetPoint{YZA}
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+ \tkzInterLL(Y,Z)(A,YZA)\tkzGetPoint{YZA}
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+ \tkzDefLine[perpendicular=through B,K=1,/tikz/overlay](Y,Z)\tkzGetPoint{YZB}
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+ \tkzInterLL(Y,Z)(B,YZB)\tkzGetPoint{YZB}
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+ \tkzDefLine[perpendicular=through C,K=1,/tikz/overlay](Y,Z)\tkzGetPoint{YZC}
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+ \tkzInterLL(Y,Z)(C,YZC)\tkzGetPoint{YZC}
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+
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+ \tkzLabelPoints[below left,font=\sansmath\sffamily](A)
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+ \tkzLabelPoints[below right,font=\sansmath\sffamily](B)
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+ \tkzLabelPoints[above,font=\sansmath\sffamily](C)
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+ \tkzLabelPoints[below left,font=\sansmath\sffamily](X)
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+ \tkzLabelPoints[above,font=\sansmath\sffamily](Z)
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+ \tkzLabelPoints[above,font=\sansmath\sffamily](Y)
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+
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+ % Draw polygon
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+ \tkzDrawPolygon[thick,fill=gray!10](A,B,C)
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+
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+ % Draw polygon
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+ \tkzDrawPolygon[thick](A,B,C)
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+
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+ \tkzDrawSegments[thick,color=blue](A,YZA B,YZB C,YZC)
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+ \tkzDrawLines[thick](A,Z)
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+ \tkzDrawLines[thick,color=red](Z,X)
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+
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+ \tkzLabelSegment[right=-0.1,color=blue](A,YZA){a}
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+ \tkzLabelSegment[right=-0.01,color=blue](B,YZB){b}
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+ \tkzLabelSegment[left=-0.1,color=blue](C,YZC){c}
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+
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+ \tkzDrawPoints[color=black,shape=circle,fill=black,size=2](A,B,C,X,Y,Z,YZA,YZB,YZC)
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+\end{tikzpicture}
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+\end{preview}
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+\end{document}
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