Question

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 $△ABC$, then $(R+r)$ is equal to

• A. $2\sqrt{2}$
• B. $3\sqrt{2}$
• C. $7\sqrt{2}$
• D. $\frac{9}{\sqrt{2}}$

Answer 1

The correct option is D $\frac{9}{\sqrt{2}}$


$r=\frac{|0+0-3|}{\sqrt{2}}=\frac{3}{\sqrt{2}}\sin {30}^{\circ }=\frac{r}{R}=\frac{1}{2}\Rightarrow R=2r\Rightarrow r+R=3r\therefore r+R=\frac{9}{\sqrt{2}}$