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If x/(b+c-a)=y/(c+a-b)=z/(a+b-c), show t...

If `x/(b+c-a)=y/(c+a-b)=z/(a+b-c)`, show that `(b-c)x+(c-a)y+(a-b)z=0`

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`x/(b+c-a)=y/(c+a-b)=z/(a+b-c)=k`
x=k(b+c-a)
y=k(c+a-b)
z=k(a+b-c)
(b-c)x+(c-a)y+(a-b)z
=k{(b+c-a)(b-c)+(c+a-b)(c-a)+(a+b-c)(a-b)}
=k{b^2-c^2-a(b-c)+c^2-a^2-b(c-a)+a^2-b^2-c(a+b)}
=k{a(c-b)+b(a-c)+c(b-a)}
...
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