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ILL 1988 Problem 69

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

    Dataset text AoPS wiki problems. Quoted with source.

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