Question 737118
Smallest or otherwise, your description is only one particular circle.  It can easily be drawn according to how you describe.  The radius is 1 unit.  Imagine this circle in the cartesian plane, centered at (1, 1) which will be tangent to the two cartesian axes at (1, 0) and at (0, 1).  


You ask for steps to finding the "largest " circle tangent to two perpendicular rays, such that the circle is radius 1.  This is only one circle.  Using standard form, filling in the information as if done on cartesian system, one possible circle is then (x-1)^2+(y-1)^2=1, and the perpendicular rays are the x and y axes in their positive directions meeting with shared endpoints at the origin.  No other steps really.


{{{graph(200,200,0,5,0,5,1+sqrt(1-(x-1)^2),1-sqrt(1-(x-1)^2))}}}