Let the centroid of an equilateral triangle \( A B C \) be at the origin. Let one of the sides o...

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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 \( \triangle A B C \), then \( (R+r) \) is equal to
(a) \( \frac{9}{\sqrt{2}} \)
(b) \( 7 \sqrt{2} \)
(c) \( 2 \sqrt{2} \)
(d) \( 3 \sqrt{2} \)
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