If a circle of a constant radius 6 passes through origin $O$ and meets the coordinate axes at $A$ and $B$, then find the locus of the centroid of $ riangle O A B$.

Question

If a circle of a constant radius 6 passes through origin $O$ and meets the coordinate axes at $A$ and $B$, then find the locus of the centroid of $	riangle O A B$.

Aicharya · Accepted Answer

Let $(h, k)$ be centroid of triangle $	herefore \quad h=\frac{a}{3}$ and $k=\frac{b}{3}$ $a=3 h, b=3 k$ Now, $A B$ is diameter of circle. $\begin{aligned} 	herefore & a^2+b^2=144 \ 	herefore & (3 h)^2+(3 k)^2=144 \Rightarrow h^2+k^2=\frac{144}{9}\end{aligned}$ $h^2+k^2=16$ $	herefore$ Locus of centroid of $	riangle O A B$ is $x^2+y^2=16$

If a circle of a constant radius 6 passes through origin $O$ and meets the coordinate axes at $A$ and $B$,…

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