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.

(x-1)^2+(y+2)^2=2