Solve for x. assume that lines which appear tangent are tangent.

Remark
Secants going through a circle form a ratio that's the same for all secants going through the circle and beginning at 1 point. See the diagram below for the ratio. Follow the Line designations carefully. This comes up many times.

General Ratio is (segment from the external point to the the first intersect point of the circumference divided by the distance from the external point to the second intercept point on the circumference).

General Ratio
Put in terms of the diagram the general ratio is (OA / OB)

Equation
OA/OB = OC/OD

Substitute and Solve
9/(9 + 11) = 10/(10 + x)
9/20 = 10/(10 + x)  Notice that you can't combine the right side. Cross Multiply

9*(10 + x) = 10 * 20  Remove the brackets on the left. Combine the right factors.
90 + 9x = 200          Subtract 90 from both sides.
9x = 200 - 90      
9x = 110                  Divide by 9
110 / 9 = 12.22