Question

In $\Delta ABC$, express x in terms of a, b, and c

• A. $\frac{ac}{b+c}$
• B. $\frac{ab}{a+c}$
• C. $\frac{bc}{a+b}$
• D. $\frac{bc}{b+c}$

Answer 1

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

$\Rightarrow$ $\angle ABC=\angle DEC={45}^o$ [ Given ]

$\Rightarrow$ $AB=a,BE=b,DC=x$ and $EC=c$ [ Given ]

In $△CDE$ and $△CAB$

$\Rightarrow$ $\angle DEC=\angle ABC$ [ Given ]

$\Rightarrow$ $\angle C=\angle C$ [ Common angle ]

$\Rightarrow$ $△CDE\sim △CAB$ [ By $AA$ similarity test ]

$\Rightarrow$ $\frac{EC}{BC}=\frac{DE}{AB}$ [ Corresponding sides of similar triangles are proportional ]

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

$\therefore$ $x=\frac{ac}{b+c}$