Cirbola!

Geometry Level 3

The figure above shows a unit circle inscribed in the parabloa \(y=x^2\). The coordinates of center of the circle inscribed can be written as \( \left( a , \dfrac bc \right) \), where \(a,b,c\) are non-negative integers with \(b,c\) coprime.

Find \(a+b+c\).

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