MCQ
In $\triangle A B C, D E \| A B$. If $A B=a, D E=x, B E=b$ and $E C=c$. Then, $x=$
- A$\frac{a c}{b}$
- ✓$\frac{a c}{b+c}$
- C$\frac{a b}{c}$
- D$\frac{a b}{b+c}$
✓
Answer
Correct option: B.
$\frac{a c}{b+c}$
(B)$\frac{a c}{b+c}$
Given that $D E \| A B$
$
\begin{array}{ll}
\therefore & \frac{A B}{D E}=\frac{B C}{E C} \\
\Rightarrow & \frac{a}{x}=\frac{b+c}{c} \Rightarrow x=\frac{a c}{b+c}
\end{array}
$
Given that $D E \| A B$
$
\begin{array}{ll}
\therefore & \frac{A B}{D E}=\frac{B C}{E C} \\
\Rightarrow & \frac{a}{x}=\frac{b+c}{c} \Rightarrow x=\frac{a c}{b+c}
\end{array}
$
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