Question

If y+z-x/b+c-a=z+x-y/c+a-b=x+y-z/a+b-c , show that x/a=y/b=z/c​

Answer 1

Answer:

Let k be the common ratio.  So

y+z-x = k(b+c-a)   ... (1)

z+x-y = k(c+a-b)   ... (2)

x+y-z = k(a+b-c)   ... (3)

Adding equations (1) and (2) gives

(y+z-x) + (z+x-y) = k( (b+c-a) + (c+a-b) )

=> 2z = 2kc  =>  z/c = k

Adding equations (2) and (3) gives

(z+x-y) + (x+y-z) = k( (c+a-b) + (a+b-c) )

=> 2x = 2ka  =>  x/a = k

Adding equations (3) and (1) gives

(x+y-z) + (y+z-x) = k( (a+b-c) + (b+c-a) )

=> 2y = 2kb  =>  y/b = k

Therefore

x/a = y/b = z/c.