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

Explanation

`x/(b+c) = y/(c+a) = z/(a + b) = (y+z-x)/(c+a+a+b-b-c)` [appliying addendo process ]
` = (y + z - x)/(2a)`
` :. ` each ratio ` = (y + z - x)/(2a) ` ……………. (1)
Again , ` x/(b +c) = y/(c +a) = z/(a+b) = (z+x-y)/(a + b + b+c-c-a)` [applying addendo process ]
` = (z = x - y)/(2b)`
` :. ` each ratio ` = (z + x - y)/(2b)` ............... (2)
Also, ` x/(b +c) = y/(c + a) = z/(a + b) = (x + y - z)/( b + c + c + a - a - b)` [applying addendo process]
` = (x + y - z)/(2c)`
` :. ` each ratio ` = (x + y -z)/(2c) ` ................... (3)
Now, from (1), (2) and (3) we get , ` (y + z - x)/(2 a) = ( z + x - y)/(2b) = (x + y - z)/(2c) `
or, ` (y + z - x)/a = (z + x - y)/b = ( + y - z)/c ` [multiplying by 2]
` :. a/(y + z-x) = b/(z + x - y) = c/(x + y - z)`