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

Options

A. `1/2`
B. 2
C. 1
D. `3/2`

Explanation

To solve the problem, we start with the given equations:

\[ \frac{a+b}{c} = \frac{b+c}{a} = \frac{c+a}{b} = K \]

This means we can express each fraction in terms of \( K \):

1. From \(\frac{a+b}{c} = K\), we can rearrange it to:
\[ a + b = Kc \quad \text{(1)} \]

2. From \(\frac{b+c}{a} = K\), we can rearrange it to:
\[ b + c = Ka \quad \text{(2)} \]

3. From \(\frac{c+a}{b} = K\), we can rearrange it to:
\[ c + a = Kb \quad \text{(3)} \]

Next, we will add all three equations (1), (2), and (3):

\[ (a + b) + (b + c) + (c + a) = Kc + Ka + Kb \]

This simplifies to:

\[ 2a + 2b + 2c = K(a + b + c) \]

Now, we can factor out the common terms:

\[ 2(a + b + c) = K(a + b + c) \]

Assuming \( a + b + c \neq 0 \), we can divide both sides by \( a + b + c \):

\[ 2 = K \]

Thus, we find that:

\[ K = 2 \]

### Final Answer:
The value of \( K \) is \( 2 \).