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Let Q be the centre of the inscribed circle of a triangle ABC. Prove that for any point P,
a(PA)^2 + b(PB)^2 + c(PC)^2 = a(QA)^2 + b(QB)^2 + c(QC)^2 + (a + b + c)(QP)^2,
where a = BC, b = CA and c = AB.

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