Question

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

• A. $x^2+y^2=9a^2$
• B. $x^2+y^2=16a^2$
• C. $x^2+y^2=a^2$
• D. None of the above

Answer 1

The correct option is D None of the above

As the center of the circumcircle of an equilateral triangle is its centroid and the distance of the centroid from the vertex of the triangle is $\frac{2}{3}$rd of its median through that vertex.

So the distance of the center from a vertex of the triangle is $\left(\frac{2}{3}\right)\times 3a=2a$

Hence, the equation of the circumcircle is $x^2+y^2=4a^2$