| In the given figure, express x in terms of a, b and c. |
 |
A) \[x=\frac{ab}{a+b}\]
B) \[x=\frac{ac}{b+c}\]
C) \[x=\frac{bc}{b+c}\]
D) \[x=\frac{ac}{a+c}\]
Correct Answer: B
Solution :
| [b] In \[\Delta KPN\]and \[\Delta KLM,\] we have |
| \[\angle KNP=\angle KML=46{}^\circ \] |
| \[\angle K=\angle K\] (Common) |
| \[\Delta KNP\tilde{\ }\Delta KML\] |
| (By \[A-A\]criterion of similarity) |
| \[\frac{KN}{KM}=\frac{NP}{ML}\] |
| \[\frac{c}{b+c}=\frac{x}{a}\,\,\,\,\Rightarrow \,\,\,\,x=\frac{ac}{b+c}\] |
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