# P and the Triangle

Geometry Level 5

Let $$P$$ be a point in triangle $$ABC$$ with area $$1$$, and let $$f(P)=PA+PB+PC$$. For every triangle $$ABC$$, let $$h_{ABC}=\min_P\big[f(P)\big]$$.

Find $$\displaystyle \min_{ABC}\left[h_{ABC}\right]^4.$$

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