olymmath

OIM 2021 Problem 4

    Let a,b,c,x,y,za,b,c,x,y,z be real numbers such that

    a2+x2=b2+y2=c2+z2=(a+b)2+(x+y)2=(b+c)2+(y+z)2=(c+a)2+(z+x)2a^2+x^2=b^2+y^2=c^2+z^2=(a+b)^2+(x+y)^2=(b+c)^2+(y+z)^2=(c+a)^2+(z+x)^2

    Show that a2+b2+c2=x2+y2+z2a^2+b^2+c^2=x^2+y^2+z^2 .

    Dataset text AI-MO AoPS. Quoted with source.

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