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Home » Thus, the ratio is $ oxed\sqrt3 $. - Abu Waleed Tea

Thus, the ratio is $ oxed\sqrt3 $. - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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Solution: First, compute the center of mass (centroid) of triangle $ A...
G = \left( \frac{0 + 6 + 3}{3}, \frac{0 + 0 + 6}{3} \right) = (3, 2)
Now compute the squared distances from each vertex to $ G $:
From $ A = (0, 0) $:
d_A^2 = (3 - 0)^2 + (2 - 0)^2 = 9 + 4 = 13
From $ B = (6, 0) $:
d_B^2 = (3 - 6)^2 + (2 - 0)^2 = 9 + 4 = 13
From $ C = (3, 6) $:
d_C^2 = (3 - 3)^2 + (2 - 6)^2 = 0 + 16 = 16
Let the influence from each village be proportional to $ \frac{1}{d^2}...

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