In the given figure, x equals:

# In the given figure, x equals:

1. A
$\frac{\mathit{ab}}{a+c}$
2. B
$\frac{\mathit{ac}}{a+b}$
3. C
$\frac{\mathit{ac}}{b+c}$
4. D
$\frac{\mathit{ab}}{b+c}$

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### Solution:

Concept: We will use the concept of similarity of two triangles. We can see that LM is parallel to ON so the triangle KLM and the triangle KON are similar and then we will use the properties that corresponding sides of similar triangles are in proportion.
In $△$s LMK and ONK
$\angle \mathit{KML}$=$\angle$ONK=46°
$\angle$K=$\angle$K (have common angles)
$△$LMK is similar to $△$ONK
$△$LMK $\sim$ $△$ONK
$\frac{\mathit{KM}}{\mathit{KN}}$=$\frac{\mathit{LM}}{\mathit{ON}}$
=$\frac{b+c}{c}$
=$\frac{a}{x}$
x=$\frac{\mathit{ac}}{b+c}$
Hence, correct option is 3

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