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  • Let the centroid of an equilateral traingle 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 <img alt="\Delta AB

Let the centroid of an equilateral traingle 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:
Option: 1 \frac{ 9}{\sqrt{2}}
Option: 2 7 \sqrt{2}
Option: 3 3 \sqrt{2}
Option: 4 2 \sqrt{2}

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

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himanshu.meshram

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