Let the equation of the circle be:



Then the tangent point (1,1) is on the circle, so



The center (h,k) lies on the line 

, so



The perpendicular distance from the center (h,k), to the tangent line, 
which is


is the radius r (in green), so



So we have the system of three equations in three unknowns:



Can you find the solution?

The solution is (h,k,r) = (-2,3,√13)

So the equation of the circle is

(x+2)2 + (y-3)2 = 13 

If you have trouble finding the solution to the system,
tell me about it in the thank you message below, and I'll
get back to you by email.  No charge.

Edwin