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

  • question_answer
    In a \[\Delta ABC,\ {{r}_{1}}<{{r}_{2}}<{{r}_{3}},\]then [EAMCET 2003]

    A) \[a<b<c\]

    B) \[a>b>c\]

    C) \[b<a<c\]

    D) \[a<c<b\]

    Correct Answer: A

    Solution :

    In a \[\Delta ABC,\,\,\,\,{{r}_{1}}<{{r}_{2}}<{{r}_{3}}\] Þ  \[\frac{1}{{{r}_{1}}}>\frac{1}{{{r}_{2}}}>\frac{1}{{{r}_{3}}}\Rightarrow \frac{s-a}{\Delta }>\frac{s-b}{\Delta }>\frac{s-c}{\Delta }\] Þ  \[s-a>s-b>s-c\Rightarrow -a>-b>-c\]Þ \[a<b<c\].


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