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JEE Main202118 Mar 2021Evening ShiftMathematicsStraight LinesActual

Let the centroid of an equilateral triangle A B C be at the origin. Let one of the sides of the equilateral triangle be along the straight line x + y = 3 . If R and r be the radius of circumcircle and incircle respectively of Δ A B C , then ( R + r ) is equal to :

Options

  1. A9 2
  2. B7 2
  3. C2 2
  4. D3 2

Correct answer

A. 9 2

Step-by-step solution

Distance from origin to line x + y = 3 is inradius. r = O M = 3 2 &   sin 30 ° = 1 2 = r R ⇒ R = 6 2 ∴ r + R = 9 2

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