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\begin{center}
\begin{tikzpicture}
\tkzDefPoint(0,0){A} \tkzDefPoint(30:4){C} \tkzDefPoint(10,0){VSH}
\tkzDrawLine(A,C) \tkzCompass(A,C)
\tkzLabelLine[above left](A,C){$b$}
\tkzInterCC(A,C)(C,A) \tkzGetPoints{K60X}{K60}
\tkzCompass(A,K60) \tkzCompass(C,K60)
\tkzDefMidPoint(C,K60) \tkzGetPoint{K30}
\tkzCompass(C,K30) \tkzCompass(K60,K30)
\tkzDrawLine(A,VSH)
\tkzLabelLine[above](A,K30){$c$}\tkzCompass(A,VSH)
\tkzInterCC(C,VSH)(VSH,C) \tkzGetPoints{PBX}{PB} \tkzDrawLine(C,VSH)
\tkzCompass(VSH,PB) \tkzCompass(VSH,PBX)
\tkzCompass(C,PB) \tkzCompass(C,PBX)
\tkzDrawLine(PB,PBX) \tkzInterLL(PB,PBX)(A,VSH) \tkzGetPoint{B}
\tkzDrawLine(C,B) \tkzDrawPolygon[fill=blue!30, opacity=.3](A,B,C)
\tkzLabelLine[below left](C,B){$a$}
\tkzCalcLength[cm](A,B)\tkzGetLength{ABl}
\tkzCalcLength[cm](B,C)\tkzGetLength{BCl}
\tkzDrawSegment[dim={\pgfmathprintnumber\ABl,-6pt,transform shape}](A,B)
\tkzDrawSegment[dim={\pgfmathprintnumber\BCl,6pt,transform shape}](C,B)
\tkzDrawPoints(A) \tkzLabelPoints(A,C,B)
\end{tikzpicture}
\end{center}
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