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    Maths-
    General
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    Question

    In triangle A B C comma blank a equals 5 comma blank b equals 4 blankandblank c equals 3. blank G is the centroid of the triangle. Circumradius of triangle G A B is equal to

    1. 2 square root of 13  
    2. fraction numerator 5 over denominator 12 end fraction square root of 13  
    3. fraction numerator 5 over denominator 3 end fraction square root of 13  
    4. fraction numerator 3 over denominator 2 end fraction square root of 13  

    The correct answer is: fraction numerator 5 over denominator 12 end fraction square root of 13

      A G equals fraction numerator 2 over denominator 3 end fraction blank A A subscript 1 end subscript comma B G equals fraction numerator 2 over denominator 3 end fraction blank B B subscript 1 end subscript
      rightwards double arrow A G equals fraction numerator 1 over denominator 3 end fraction blank square root of 2 b to the power of 2 end exponent plus 2 c to the power of 2 end exponent minus a to the power of 2 end exponent end root

      andblank B G equals fraction numerator 1 over denominator 3 end fraction square root of 2 a to the power of 2 end exponent plus 2 c to the power of 2 end exponent minus b to the power of 2 end exponent end root
      rightwards double arrow A G equals fraction numerator 1 over denominator 3 end fraction blank a comma blank B G equals fraction numerator 1 over denominator 3 end fraction square root of b to the power of 2 end exponent plus 4 c to the power of 2 end exponent end root blank a s blank a to the power of 2 end exponent equals b to the power of 2 end exponent plus c to the power of 2 end exponent
      rightwards double arrow A G equals fraction numerator 5 over denominator 3 end fraction comma blank B G equals fraction numerator 1 over denominator 3 end fraction square root of 16 plus 36 end root equals fraction numerator 2 over denominator 3 end fraction blank square root of 13
      Also,blank A B equals c equals 3 andblank increment subscript G A B end subscript equals fraction numerator 1 over denominator 3 end fraction blank increment subscript A B C end subscript equals 2
      If R subscript 1 end subscript is the circumradius of triangle G A B comma then
      R subscript 1 end subscript equals fraction numerator open parentheses A G close parentheses open parentheses B G close parentheses open parentheses A B close parentheses over denominator 4 increment subscript G A B end subscript end fraction equals fraction numerator 5 over denominator 3 end fraction cross times fraction numerator 2 over denominator 3 end fraction square root of 13 cross times 3 cross times fraction numerator 1 over denominator 4 cross times 2 end fraction equals fraction numerator 5 square root of 13 over denominator 12 end fraction blank u n i t s

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