Which point?

Geometry Level 3

A point \(P\) is located in triangle \(ABC.\) Let \(X, Y, Z\) be the feet of the perpendiculars dropped from \(P\) to sides \(BC, CA, AB,\) respectively. If \(PX + PY + PZ = 2017,\) find the minimum possible value of \(PA + PB + PC.\)

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