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由 thepiano »
令 AB = CD = 2x,AD = BC = 2y
則 DF = x,DE = y
BE = 5,BF = 10,∠EBF = 60 度,易知 EF = 5√3
cos∠EDF = (x^2 + y^2 - 75) / (2xy)
cos∠BCF = (x^2 + 4y^2 - 100) / (4xy)
cos∠BAE = (4x^2 + y^2 - 25) / (4xy)
由 (x^2 + y^2 - 75) / (2xy) = - (x^2 + 4y^2 - 100) / (4xy) = - (4x^2 + y^2 - 25) / (4xy)
可求出 x = 10/3
AB = 20/3