Coordinates and circles and triangles, oh my

Geometry Level 3

Let circle \(A\) be a circle with radius \(\sqrt{5}\) centered at \((2,0)\) and circle \(B\) be a circle with radius \(2\) centered at \((-1,0)\) Let the center of circle \(A\) be \(A_C\) and the center of circle \(B\) be \(B_C\). The two circles \(A\) and \(B\) intersect at points \(X\) and \(Y\). When the area of quadrilateral \(X A_C Y B_C\) is expressed in the form \(a \sqrt{b} \) where \(b\) is nor divisible by the square of any prime, find \(a+b\)

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