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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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Trevor Arashiro by Trevor Arashiro
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