$A = (cos θ, sin θ)$ , $b = (sin θ, - cos θ)$ , $O = (0, 0)$ are $3$ points. The centroid of the triangle O $A B$ lies on the circle whose radius is

\sqrt{\frac{2}{3}}

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\sqrt{2}

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\frac{\sqrt{2}}{3}

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\frac{1}{\sqrt{3}}

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Solution

The correct option is C $\frac{\sqrt{2}}{3}$
Centroid of $Δ A B O,$
$x = \frac{cos θ + sin θ}{3} a n d y = \frac{sin θ - cos θ}{3} \cdot$
$∴ 9 x^{2} + 9 y^{2} = 1 + 1$
$x^{2} + y^{2} = \frac{2}{9}$
Locus of centroid of $Δ A o B$ is $x^{2} + y^{2} = \frac{2}{9}$ circle.
$\Rightarrow$ radius of circle $= \frac{\sqrt{2}}{3} \cdot$

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