Let XY be a tangent to a circle, and let XA be a secant of the circle, as shown below. If AX = 15 and XY = 9, then what is AB?

Sorry, I forgot to post my diagram -

By power of a point, AB = 29/3.

There is a simple ratio formula fo this. I have seen Heureka use it. I've forgetton what it is though.

It is the middle one

In your case

9^2=XB * 15

81 = XB *15

XB = 81/15 = 5.4 units