Question

If \( \frac{a}{b+c} = \frac{b}{c+a} = \frac{c}{a+b} = r \), then \( r \) cannot take any value except.

• A. \( \frac{1}{2} \)
• B. -1
• C. \( \frac{1}{2} \) or -1
• D. \( -\frac{1}{2} \) or -1

Hint:

For such fractional equations, try to manipulate the ratios to eliminate one of the variables and check for feasible values.

Answer 1

The Correct Option is A

From the given relations, we can derive that the only possible value of \(r\) is \( \frac{1}{2} \). Other values do not satisfy the equality condition for all terms in the equation. \[ \boxed{\frac{1}{2}} \]