# Just like Gianlino's Disc. Only 1000 times easier

Geometry Level 5

Points $$A$$ and $$B$$ are placed at $$(2,0)$$ and $$(-2,0)$$ respectively. A circle of radius 3 is then drawn centered at the origin.

Next, a point $$E$$ is randomly placed on the circumference of circle C centered at the origin with radius 1.

If the probability that the circumcenter of $$\triangle ABE$$ lies within the circle of radius 3 can be represented by $$\dfrac{m}{n}$$ where $$m,n$$ are coprime positive integers, find m+n.

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