Question

If `x/(b + c - a) = y/(c + a - b) = z/(a + b - c)`  prove that each ratio’s equal to : `(x + y + z)/(a + b + c)`

Answer 1

`x/(b + c - a) = y/(c + a - b) = z/(a + b - c)` = k(say)
x = k(b + c – a),
y = k(c + a – b),
z = k(a + b – c)
`(x + y + z)/(a + b + c)`

= `(k(b + c - a) + k(c + a - b) + k(a + b - c))/(a + b + c)`

= `(k(b+ c- a + c + a - b + a  + b - c))/(a +b + c)`

= `(k(a + b + c))/(a + b + c)`
= k.
Hence proved.