Remark
ED is a tangent line. EF is a secant line. Secants and Tangents are related by the formula Tangent length ^2 from a point = length from the same point to the closest part of the circumfrence * the entire length of the secant.
Formula
Putting that long sentence into symbols
ED^2 = EG * EF
Givens
EG = 9
EF = 9 + x
ED = 12
Sub and solve
12^2 = 9*(9 + x) You can either divide by 9 or remove the brackets. I will divide by 9
144 / 9 = 9 * (9 + x) /9
16 = x + 9 Subtract 9 from both sides.
x = 7
x = 7 units. <<<<<<<< Answer