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\begin{tikzpicture}[scale=1.25]
\tkzDefPoint(0,0){O}
\tkzDefPoint(2.5,0){N}
\tkzDefPoint(-4.2,0.5){M}
\tkzDefPointBy[rotation=center O angle 30](N)
\tkzGetPoint{B}
\tkzDefPointBy[rotation=center O angle -50](N)
\tkzGetPoint{A}
\tkzInterLC(M,B)(O,N) \tkzGetFirstPoint{C}
\tkzInterLC(M,A)(O,N) \tkzGetSecondPoint{A'}
\tkzMarkAngle[mkpos=.2, size=0.5](A,C,B)
\tkzMarkAngle[mkpos=.2, size=0.5](A,M,C)
\tkzDrawSegments(A,C M,A M,B)
\tkzDrawCircle(O,N)
\tkzLabelCircle[above left](O,N)(120){$\mathcal{C}$}
\tkzMarkAngle[mkpos=.2, size=1.2](C,A,M)
\tkzDrawPoints(O, A, B, M, B, C)
\tkzLabelPoints[right](O,A,B)
\tkzLabelPoints[above left](M,C)
\tkzLabelPoint[below left](A'){$A'$}
\end{tikzpicture}
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