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

  • question_answer
    If R is the radius of the circumcircle of the \[\Delta ABC\]and \[\Delta \]is its area, then [Karnataka CET 2000]

    A) \[R=\frac{a+b+c}{\Delta }\]

    B) \[R=\frac{a+b+c}{4\Delta }\]

    C) \[R=\frac{abc}{4\Delta }\]

    D) \[R=\frac{abc}{\Delta }\]

    Correct Answer: C

    Solution :

    Area of the triangle ABC \[(\Delta )=\frac{bc}{2}\sin A.\] From the sine formula, a = 2R sin A or \[\sin A=\frac{a}{2R}.\] \[\Rightarrow \,\,\Delta =\frac{1}{2}bc\,.\,\frac{a}{2R}=\frac{abc}{4R}\,\text{or }R=\frac{abc}{4\Delta }.\]


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