A tangent circle to a parabola

Calculus Level 4

Let \( y = \dfrac{x^2 } 4 \). A circle is tangent to this parabola at \( x_0 = 2 \), and also tangent to the \(y\)-axis. If \( r \) is the radius of this circle, find \( \lfloor 100 r \rfloor \).

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