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The figure shows the graph of f(x)=x−1xf(x)=x-\frac{1}{x}f(x)=x−x1.
The circle is tangent to the graph in domain x<0x<0x<0 and x>0x>0x>0, and is the smallest of its kind.
The area of the circle is in the form Aπ(−B+C)A\pi \left( -B+\sqrt { C } \right) Aπ(−B+C) where A,B,CA,B,CA,B,C are positive integers with CCC square free.
Find A+B+CA+B+CA+B+C.
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