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Consider an equilateral triangle having vertices at the points `A(2/(sqrt(3))e^(ipi/2)),B(2/(sqrt(3))e^(-ipi/6)),C(2/(sqrt(3))e^(-i(5pi)/6)),` Let `P` be any point on its incircle, Prove that `A P^2+B P^2+C P^2=5.`

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