Question 327055
If we draw a picture, we can see that the radius of the wheel has length 

R=10+x or R=5+y............[1]

The equation of a circle is {{{x^2+y^2=R^2}}}

From [1], we see that x=R-10 and y=R-5

This gives us 

{{{(R-10)^2+(R-5)^2=R^2}}}

Now, we have to down to one variable.

Simplify and form a quadratic:

{{{R^2-30R+125=0}}}

{{{R=5}}}
{{{R=25}}}

Of course, 5 is extraneous and we find the wheel has radius 25 inches.