If a/(b + c) = b/(c + a) = c/(a + b) = K, then the value of K is -

Question: If a/(b + c) = b/(c + a) = c/(a + b) = K, then the value of K is -

Solution:
a/(b + c) = K
Or, a = K(b + c) --------- (1)
b/(c + a) = K
Or, b = K(c + a) --------- (2)
c/(a + b) = K
Or, c = K(a + b) --------- (3)

Adding (1) , (2) and (3) we get,
a + b + c = K(2a + 2b + 2c)
Or, K = (a + b + c)/2 (a + b + c)
∴ K = 1/2