In RT △ ABC, ∠ ACB = 90 °, ∠ BAC = 30 °, BC = 1, P is a point in △ ABC, and ∠ APC = ∠ BPC = ∠ APB = 120, calculate the value of PA + Pb + PC

Let PA = x, Pb = y, PC = Z, ﹥ APB = ﹥ BPC = ﹥ CPA = 120 degrees, then by the cosine theorem x ^ 2 + y ^ 2 + xy = C ^ 2Y ^ 2 + Z ^ 2 + YZ = a ^ 2Z ^ 2 + x ^ 2 + XZ = B ^ 2, add three formulas (x + y + Z) ^ 2 = (a ^ 2 + B ^ 2 + C ^ 2 + 3 (XY + YZ + ZX)) / 2. (1) by the sine theorem √ 3xy / 4 = s

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1. In the tetrahedral PABC, PA = Pb = PC = 2, APB = BPC = APC = 30 degree In the tetrahedral PABC (P is the vertex), PA = Pb = PC = 2, ∠ APB = ∠ BPC = ∠ APC = 30 °, starting from point a, circling along the tetrahedral surface, and then returning to point a, the shortest distance is
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