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JEE Main 202118 MarchEvening Shift
Exam
JEE Main
Year
2021
Date
18 March
Shift
Evening Shift
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2021 · 18 March · Evening Shift · Mathematics · Straight Lines

Let the centroid of an equilateral triangle ABC be at the origin....

Let the centroid of an equilateral triangle ABCABC be at the origin. Let one of the sides of the equilateral triangle be along the straight line x+y=3x + y = 3. If RR and rr be the radius of circumcircle and incircle respectively of δABC\delta ABC, then (R+r)( R + r ) is equal to :Let the centroid of an equilateral triangle ABC be at the origin. Let one of the sides of the equilateral triangle be

Options

  1. A92\dfrac{9}{\sqrt{2}}
  2. B727\sqrt{2}
  3. C222\sqrt{2}
  4. D323\sqrt{2}

Correct answer

A. 92\dfrac{9}{\sqrt{2}}

Step-by-step solution

Let the centroid of an equilateral triangle ABC be at the origin. Let one of the sides of the equilateral triangle be

Distance from origin to line x+y=3x + y = 3 is inradius.

r=OM=32r = OM = \dfrac{3}{\sqrt{2}}

 and sin⁡30°=12=rR⇒R=62\text{ and } \sin 30 ° = \dfrac{1}{2} = \dfrac{r}{R} ⇒ R = \dfrac{6}{\sqrt{2}}

∴r+R=92∴ r + R = \dfrac{9}{\sqrt{2}}

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