Question

In the given figure, $x$ is

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

Answer 1

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

In $△KPN$ and $△KLM,\angle K$ is common and we have
$$\angle KNP=\angle KML={46}^{\circ }$$
Thus by $A-A$ criterion of similarity,
$$\begin{array}{cc}\Delta KNP& \sim \Delta KML\\ \frac{KN}{KM}& =\frac{NP}{ML}\\ \frac{c}{b+c}& =\frac{x}{a}\Rightarrow x=\frac{ac}{b+c}\end{array}$$
Thus (b) is correct option.