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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 17

  • question_answer
    In a triangle ABC, if \[\angle ABC=60{}^\circ \] and r is in radius, then \[{{\left( \frac{AB-BC+CA}{r} \right)}^{2}}=\]

    A) 6                      

    B)        12        

    C) 16                    

    D)        20

    Correct Answer: B

    Solution :

    [b] \[r=\tan \left( \frac{A}{2} \right)\left( s-a \right)\] \[\Rightarrow \,\,\,r=\frac{1}{\sqrt{3}}\,\,\left( \frac{AB+BC+CA}{2}-BC \right)\] \[\Rightarrow \,\,\,\,{{\left( \frac{AB-BC+CA}{r} \right)}^{2}}=12\]          


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