Question 971370
This response is not a full solution.


Line of tangency is also y=2x+1;
Line containing center is also y=-x+9;


Try to sketch as much of the graph as you can do.


There is a line with slope  {{{-1/2}}} through point (2,3) which intersects with the line y=-x+9.  That intersection point is the center of the circle.


Distance from  (2,3) to the center point of circle gives the size of the radius.