Hi Bharathi,
I presume you have the center of the circle (h, k) as well. Here's how I would do this. The gist is to convert it to a polar coordinate system, rotate to find the other two points, then convert back to cartesians.
 Apply the transformation x x  h and y y  k to slide the centre to the origin.
 Switch to polar coordinates (r, θ) using the relationship θ = tan^{1}(y/x).
 Apply two 120^{o} angular transformations to find the two other points in polar form (r, θ_{i}).
 Convert both new points back to the cartesian coordinates using the relationships x_{i} = r cos(θ_{i}) and y_{i} = r sin(θ_{i}).
 Apply the transformation x_{i} x_{i} + h and y_{i} y_{i} + k for both points to move the centre back.
Hope this helps,
Stephen La Rocque.
