Connect the curve 2

Calculus Level 3

The figure shows the graph of f(x)=x1xf(x)=x-\frac{1}{x}.

The circle is tangent to the graph in domain x<0x<0 and x>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) where A,B,CA,B,C are positive integers with CC square free.

Find A+B+CA+B+C.

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