Are you stronger than a 5th standard pass-out?

Geometry Level pending

In a triangle \(ABC,\) \(AB = \sqrt{3},\) \(BC=1,\) and \(CA = 2.\) Consider the point \(P\) which is in the same plane as \(\triangle ABC\) that minimizes \(AP+BP+CP.\) Find \(\left(AP+BP+CP\right)^2.\)

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