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 \(a + b\).
by
Brian Charlesworth