Connect the curve 2

Calculus Level 4

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

The circle is tangent to the graph in domain \(x<0\) and \(x>0\), and is the smallest of its kind.

The area of the circle is in the form \[A\pi \left( -B+\sqrt { C } \right) \] where \(A,B,C\) are positive integers with \(C\) square free.

Find \(A+B+C\).

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