Question 759509
If the wheel is resting on the floor and against the wall, the tangent lines are x=0 and y=0 and the points of tangency are (r,0) and (0,r).  
The equations for the lines perpendicular to these tangent lines at these points are x=r and y=r and they must go through the center of the circle.
So the center of the circle is (r,r)
The standard form for a circle is (x-a)^2 + (y-b)^2 = r^2 where (a,b) is the center and r is the radius
Since the point P is 2 cm from the floor and 9 cm from the wall, the point is (9,2)
Inserting the point (9,2) in the equation for the circle gives
(9-r)^2 (2-r)^2 = r^2
Simplify and solve for r:
81 - 18r + r^2 + 4 - 4r + r^2 = r^2
r^2 - 22r + 85 = 0
This can be factored as 
(r-17)(r-5) = 0
This gives two possible solutions, r=5 cm and r=17 cm
The graph below shows the two circles which share the point (9,2)
{{{drawing( 400, 400, -4, 38, -4, 38,
  grid( 1 ),
  red( circle( 5, 5, 5 ) ),
  blue( circle(9, 2, 0.3) ),
  green( circle( 17, 17, 17 ) ))}}}