In given figure, express x in terms of a, b and c.

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Solution

In $△ K P N$ and $△ K L M$ , we have

$∠ K N P = ∠ K M L = 46^{\circ}$ [Given]

$∠ K = ∠ K$ [Common]

$∴$ $△ K N P \sim △ K M L$ [By AA-criterion of similarity]

$\Rightarrow$ $\frac{K N}{K M} = \frac{N P}{M L}$ [ $∵$ Corresponding sides of similar triangles are proportional]

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

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

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In figure, express x in terms of a,b and c.

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