Just like Gianlino's Disc. Only 1000 times easier

Geometry Level 5

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

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

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

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