2021 OIM Problems/Problem 4
Problem
Let 
be real numbers such that
![\[a^2+x^2=b^2+y^2=c^2+z^2=(a+b)^2+(x+y)^2=(b+c)^2+(y+z)^2=(c+a)^2+(z+x)^2\]](http://latex.artofproblemsolving.com/b/f/f/bfff796c3b6ba4c7d7a4ce071aed963145cf5028.png)
Show that 
Solution
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