Question

y/b+c-a= z/c+a-b=x/a+b-c then prove that a/z+x=b/x+y=c/y+z

Answer 1

Hello friend

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Here is your answer!!

==> By using invertendo,we get

Now let b+c-a/y = c+a-b/z = a+b-c/x= k

By theorem of equal ratios,

$k = \frac{(c + a - b) + (a + b - c)}{z + x} \\ \\ = \frac{2a}{z + x} \: \: \: ...............(i) \\ \\ \\ k = \frac{( a + b - c) + (b + c - a)}{x + y} \\ \\ = \frac{2b}{x + y} \: \: \: \: ..................(ii) \\ \\ \\ k = \frac{(b + c - a) + (c + a - b)}{y + z} \\ \\ = \frac{2c}{y + z} \: \: \: .....................(iii) \\ \\ \\ \\ \frac{2a}{z + x} = \frac{2b}{x + y} = \frac{2c}{y + z} \\ \\ \\ \frac{a}{z + x} = \frac{b}{x + y} = \frac{c}{y + z}$

We have proved,

Thanks....

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