The red line is the tangent line.
The green line is where the center lies on.
A circle dot represents a point which lies on the circle.
A rhombus dot represents the center of circle.
This is what I did.
1)Drew the red line and green line and circle dot (given to us).
2)Pick a point (x,y) on the green line and find locus that is equidistanct from the intersection point (1/3,-2/3) and the dot (2,-1).
3)The locus was a line (not show), it intersected the green line at (1,-2)-the rhombus dot, and that was the center of circle.
4)Now we have a center (1,-2) and a point on it (2,-1) we can find the distance, sqrt(2), and find the equation of circle.