JEE Main & Advanced Mathematics Trigonometric Equations Question Bank Circle connected with triangle

  • question_answer
    If the sides of a triangle are in ratio 3 : 7 : 8, then R : r is equal to  

    A) 2 : 7

    B) 7 : 2

    C) 3 : 7

    D) 7 : 3

    Correct Answer: B

    Solution :

    Let \[a=3k,\,b=7k,\,c=8k\] \[\therefore \] \[s=\frac{1}{2}(a+b+c)=9k\] Then \[\frac{R}{r}=\frac{abc}{4\Delta }.\frac{s}{\Delta }=\frac{abc.s}{4s(s-a)\,(s-b)\,(s-c)}\]              =\[\frac{3k\,.\,7k.\,8k}{4.\,6k\,.\,2k\,.\,k}=\frac{7}{2}\]  i.e., \[R:r=7:2\].


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