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AP EAMCET202317 May 2023Evening ShiftMathematicsStraight LinesActual

Let origin be the centroid of an equilateral triangle ABC and one of its sides be along the straight line x+y=3 . If R and r are its circum radius and inradius respectively, then R + r =

Options

  1. A2 2
  2. B9 2
  3. C7 2
  4. D3 2

Correct answer

B. 9 2

Step-by-step solution

Given that one of the sides of the equilateral triangle be along the straight line x+y=3 And we know in an equilateral triangle each side have an angle 60^ . OBM = 60^ 2 =30^ From the figure, r= OM = perpendicular distance O(0,0) & x+y=3 r= | (0+0-3) 1+1 |= 3 2 ...(i) Now, r+ R = 3 2 + 6 2 = 9 2

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