# A geometry problem by Neel Khare

Geometry Level 3

Let $$A,B$$ and $$C$$ be the angles of an acute-angled triangle. If the minimum value of $$\tan A \tan B \tan C$$ can be expressed as $$m \sqrt n$$, where $$m$$ and $$n$$ are positive integers with $$n$$ square-free, find $$m^2+n^2-18$$.

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