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AP EAMCET20226 Jul 2022Morning ShiftMathematicsStraight LinesActual

The length of the sides of a triangle are 13,14 & 15 . If R and r respectively denote circumradius and inradius of this triangle, then 8 R - r =

Options

  1. A41
  2. B51
  3. C61
  4. D71

Correct answer

C. 61

Step-by-step solution

Given sides of triangle are 13, 14, 15 Circumradius (R)= a b c 4 Inradius ( r )= 5 aligned & = ( 13+14+15 2 ) ( 13+14+15 2 -13 ) ( 13+14+15 2 -14 ) ( 13+14+15 2 -15 ) & = 21 8 7 6 = 7056 =84 aligned From (i) Circumradius ( R )= 13 14 15 4 84 = 195 24 Inradius (r) = 84 42 2=4 Now, 8 R - r =8 195 24 -4=65-4=61 .

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