The equation of the circle with the origin as | vedclass

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(D) For an equilateral triangle,the centroid coincides with the circumcentre.Given the origin $(0, 0)$ is the centre of the circle passing through the

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None of these

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(D) For an equilateral triangle,the centroid coincides with the circumcentre.Given the origin $(0, 0)$ is the centre of the circle passing through the vertices,it is the circumcentre of the triangle.The centroid divides the median in the ratio $2:1$.Since the length of the median is $3a$,the distance from the centroid to the vertex (which is the radius $R$ of the circumcircle) is $R = \frac{2}{3} 	imes 3a = 2a$.The equation of the circle with centre $(0, 0)$ and radius $R = 2a$ is $x^2 + y^2 = (2a)^2 = 4a^2$.Since $4a^2$ is not among the given options,the correct answer is $(d)$.

The equation of the circle with the origin as the centre passing through the vertices of an equilateral triangle whose median is of length $3a$ is

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