Question

If $\frac{a}{b+c}$ = $\frac{b}{c+a}$ = $\frac{c}{a+b}$ and $a+b+c\ne$ 0, value of $a$ is .

• A. $\frac{b+c}{2}$
• B. $\frac{1}{2}$
• C. $2\times (b+c)$
• D. $2\times \left(b\right)$

Answer 1

The correct option is A $\frac{b+c}{2}$

As per the theorem of equivalent ratio,

$\frac{a}{b+c}$ = $\frac{b}{c+a}$ = $\frac{c}{a+b}$ = $\frac{a+b+c}{b+c+c+a+a+b}$

= $\frac{a+b+c}{2(a+b+c)}$ = $\frac{1}{2}$

$⟹$ a = $\frac{b+c}{2}$