# Shocked Face

Geometry Level 5

Let $$R$$ be the region in the first quadrant outside of the circles $$x^{2} + y^{2} = 4$$ and $$x^{2} + (y - 3)^{2} = 1$$ but inside the circle $$x^{2} + (y - 1)^{2} = 9.$$

The largest circle that can be inscribed in $$R$$ has radius $$\dfrac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers. Find $$a + b$$.

×