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

It is given that the triangle is equilateral. Therefore, centroid of the triangle is same as the circumcircle.Also, Radius of the circumcircle =23 (median) =23(3a)=2aHence, the equation of the circumcircle whose centre is at(0, 0) and radius 2a, is x2+y2=(2a)2