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\begin{tikzpicture}[scale=.5]
\tkzDefPoint(0,8){A} \tkzDefPoint(8,0){B}
\tkzDefPoint(8,8){C} \tkzDefPoint(4,4){I}
\tkzDefPoint(2,7){E} \tkzDefPoint(6,4){F}
\tkzDrawCircle[R](I,4 cm)
\tkzInterLC[R](A,C)(I,4 cm) \tkzGetPoints{I1}{I2}
\tkzInterLC[R](B,C)(I,4 cm) \tkzGetPoints{J1}{J2}
\tkzInterLC[R](A,B)(I,4 cm) \tkzGetPoints{K1}{K2}
\tkzDrawPoints[color=red](I1,J1,K1,K2)
\tkzDrawLines(A,B B,C A,C)
\tkzInterLC[R](E,F)(I,4 cm) \tkzGetPoints{I2}{J2}
\tkzDrawPoints[color=blue](E,F)
\tkzDrawPoints[color=red](I2,J2)
\tkzDrawLine(I2,J2)
\end{tikzpicture}
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