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\begin{tikzpicture}[scale=.5]
\tkzDefPoint(2,3){A} \tkzDefPoint(5,-1){B}
\tkzDefPoint[label=below:$\mathcal{C}$,
shift={(2,3)}](-30:5.5){E}
\begin{scope}[shift=(A)]
\tkzDefPoint(30:5){C}
\end{scope}
\tkzCalcLength[cm](A,B)\tkzGetLength{rAB}
\tkzDrawCircle[R](A,\rAB cm)
\tkzDrawSegment(A,B)
\tkzDrawPoints(A,B,C)
\tkzLabelPoints(B,C)
\tkzLabelPoints[above](A)
\end{tikzpicture}
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