# What are we in?

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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