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

The origin or the center of the circle must act as the centroid of the equilateral trianlge . So,it must divide the median int 2:1. So the distance of the vertex of the triangle form the center is 2a,which will act as the radius of the circle. So the equation must be x^2+y^2=4a^2

Hi Abhi,

Let r be the radius of the circle.

As median will pass through the centre of the circle, and median is divided in the ratio 2:1 at the centre (which would be the centroid).

So r = 2a.

Hence Eqn of Circle : x^2 + y^2 = (2a)^2.

Hope that helps.

Best Regards,

Ashwin (IIT Madras).