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

  • question_answer
    The radius of the in circle of triangle when sides are 18, 24 and 30 cms is [Pb. CET 2004]

    A) 2 cm

    B) 4 cm

    C) 6 cm

    D) 9 cm

    Correct Answer: C

    Solution :

    \[r=\frac{\text{Area of triangle}}{s}=\frac{\Delta }{s}\] \[s=\frac{a+b+c}{2}=\frac{18+24+30}{2}\], \[s=36\] \[\Delta =\sqrt{s(s-a)\,(s-b)\,(s-c)}\] \[\Delta =\sqrt{36\,(36-18)\,(36-24)\,(36-30)}\] \[\Delta =\sqrt{36\times 18\times 12\times 6}=216\] So, radius of in circle = \[\frac{216}{36}=6cm\].


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