A) \[\frac{4}{9}\]
B) \[\frac{6}{7}\]
C) \[\frac{1}{4}\]
D) \[\frac{2}{9}\]
Correct Answer: D
Solution :
\[\frac{AB}{AP}=\frac{1}{2}\] Let \[\angle APC=\alpha \] \[\tan \theta =\frac{AC}{AP}=\frac{1}{2}\frac{AB}{AP}=\frac{1}{4}\] \[\left( AC=\frac{1}{2}AB \right)\] Now \[\tan (\alpha +\beta )=\frac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }\] \[\frac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }=\frac{1}{2}\left[ \begin{matrix} \tan (\alpha +\beta )=\frac{AB}{AP} \\ \tan (\alpha +\beta )=\frac{1}{2} \\ \end{matrix} \right]\] on solving \[\tan \beta =\frac{2}{9}\]You need to login to perform this action.
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