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BCECE Engineering BCECE Engineering Solved Paper-2008

  • question_answer
    If in \[\Delta \,ABC,\,\,\tan \frac{A}{2}=\frac{5}{6}\] and \[\tan \frac{C}{2}=\frac{2}{5},\]then\[a,b,c\] are such that

    A) \[{{b}^{2}}=ac\]    

    B) \[2b=a+c\]           

    C) \[2ac=b(a+c)\]

    D) \[a+b=c\]

    Correct Answer: B

    Solution :

    Since, \[\tan \frac{A}{2}=\frac{5}{6}\]and \[\tan \frac{C}{2}=\frac{2}{5}\] \[\therefore \]  \[\tan \frac{A}{2}\tan \frac{C}{2}=\frac{5}{6}.\frac{2}{5}\] \[\Rightarrow \]\[\sqrt{\frac{(s-b)(s-c)}{s(s-a)}}\times \sqrt{\frac{(s-a)(s-b)}{s(s-c)}}=\frac{1}{3}\] \[\Rightarrow \]               \[\frac{s-b}{s}=\frac{1}{3}\] \[\Rightarrow \]               \[3s-3b=s\] \[\Rightarrow \]               \[2s=3b\] \[\Rightarrow \]               \[a+c=2b\]


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