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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