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Geometry Level 3

Perpendicular cords \(AC\) and \(DE\) intersect at \(B\) so that the lengths of \(AB,BC\) and \(BD\) are 3, 4 and 2 respectively. If the radius of the circle can be written as \( \dfrac{\sqrt m} n \), where \(m\) and \(n\) are positive integers with \(m\) square-free. Find \(m+n\).

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