| In the figure, find x in terms of a, b and c. |
 |
A) \[\frac{ab}{a+c}\]
B) \[\frac{ac}{b+c}\]
C) \[\frac{bc}{a+b}\]
D) \[\frac{ac}{a+b}\]
Correct Answer: B
Solution :
| [b] In \[\Delta KNP\] and \[\Delta KML\] |
| \[\angle KNP=\angle KML=35{}^\circ \] (Given) |
| \[\angle K=\angle K\] (Common) |
| \[\therefore \,\,\,\,\,\,\,\,\Delta KNP\tilde{\ }\Delta KML\] |
| (By AA similarity criterion) |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{PN}{LM}=\frac{KN}{KM}\] |
| (Corresponding sides of similar triangles are proportional) |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\frac{x}{a}=\frac{c}{KN+NM}=\frac{c}{c+b}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,x=\frac{ac}{b+c}\] |
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