It is known that ABC is a real number and B + C of a = C + a of B = a + B of C = K? If the title, seek detailed explanation

It is known that ABC is a real number and B + C of a = C + a of B = a + B of C = K? If the title, seek detailed explanation

Reverse the three formulas to get
(b+c)/a=(a+c)/b=(a+b)/c
Add one to each formula
(a+b+c)/a=(a+b+c)/b=(a+b+c)/c
That is, a = b = C, so k = 1 / 2