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2021 OIM Problems/Problem 4

Problem

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

\[a^2+x^2=b^2+y^2=c^2+z^2=(a+b)^2+(x+y)^2=(b+c)^2+(y+z)^2=(c+a)^2+(z+x)^2\]

Show that $a^2+b^2+c^2=x^2+y^2+z^2$

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also

https://olcoma.ac.cr/internacional/oim-2021/examenes

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