# 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 $$a+b$$

×