Well there is probably a much easier way to complete this problem but here is my suggestion. Think of the walls as the x and y-axes. The circle is tangent to both the x and y-axes. Let the x-axis tangent point be (x, 0) and let the y-axis tangent point be (0, y). Then the center must be (x, y). Since the radii of a circle are constant, x = y.
We are also told that there is a point on the circle which is 9 units away from one of the axes and 2 units away from the other axis. This is equal to the points (9, 2) or (2, 9).
As I mentioned before, the radii of a circle are constant so the distance from the center (x, y) to the x-axis tangent point (x, 0) must be equal to the distance from the center (x, y) to one of those previously given points. It does not matter which one you use so let's just say (9, 2). Apply the distance formula and equate them.
sqrt[(x-9)^2+(y-2)^2] = sqrt[(x-x)^2+(y-0)^2]
(x-9)^2+(y-2)^2 = (x-x)^2+(y-0)^2
(x-9)^2+(x-2)^2 = (x-x)^2+(x-0)^2
x^2-18x+81+x^2-4x+4 = x^2
x^2-22x+85 = 0
(x-5)(x-17) = 0
x= 5, 17
5 can be eliminated because if the radius were 5, the points (9, 2) and (2, 9) could not exist between the x and y axes tangent points as the problem requires. Therefore the radius of the circle is 17inches.
I know it's hard to picture all of this without a drawing so it will help if you draw a simple diagram. If you have any questions about all of this, feel free to ask. Like I said earlier, there is probably a much easier way to complete this problem.
