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

Options

A. `x^(2)+y^(2)=9a^(2)`
B. `x^(2)+y^(2)=16a^(2)`
C. `x^(2)+y^(2)=4a^(2)`
D. `x^(2)+y^(2)=a^(2)`

Answer

C

Explanation

It is given that the triangle is equilateral .
Therefore, centroid of the triangle is same as the circumcentre.
Also, Radius of the circumcircle `=(2)/(3)`(Median)`=(2)/(3)(3a)=2a`
Hence, the equation of the circumcircle whose centre is at (0, 0) and radius `2a, ` is `x^(2)+y^(2)=(2a)^(2)`.