JEE Main 2021 (Online) 18th March Evening ShiftQuestion 1
Let the centroid of an equilateral triangle $ABC$ 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 $\triangle ABC$, then $(R+r)$ is equal to :
Points and Straight Lines
Solution
Centroid = incentre = circumcentre = origin. $r=$ distance of $x+y=3$ from origin $=\frac{3}{\sqrt2}$. $R=2r=\frac{6}{\sqrt2}$. $R+r=3r=\frac{9}{\sqrt2}$. Option (B).