if x÷b+c-a =y÷c+a-b=z÷a+b-c then (b-c)x +(c+a)y +(a- b) z=
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⇒ 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)}<br> =k{b^2-c^2-a(b-c)+c^2-a^2-b(c-a)+a^2-b^2-c(a+b)}<br> =k{a(c-b)+b(a-c)+c(b-a)}<br> =k{0}=0.
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