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  4. 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 Δ ABC, then ( R + r ) is equal to :

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Q. 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 $\Delta ABC$, then $( R + r )$ is equal to :

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Solution:

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$r = OM =\frac{3}{\sqrt{2}}$
$\& \sin 30^{\circ}=\frac{1}{2}=\frac{ r }{ R } \Rightarrow R =\frac{6}{\sqrt{2}}$
$\therefore r + R =\frac{9}{\sqrt{2}}$