AO is the radius of the circle, so both AO and CO have the same measurement in length. This means that to find the length of BO, you can just add BC + CO and plug in the radius of 17 for CO and the given measure of 128 for BC.
128 + 17 = 145
Now that you have the measure of two of the legs of the triangle, and the triangle is a right triangle, you can use the Pythagorean Theorem. Plug in what you know to find the missing length.
****Note that BO is the hypotenuse, so c = 145. ***************************
a^2 + b^2 = c^2
17^2 + b^2 = 145^2
289 + b^2 = 21,025 (Subtract 289 from both sides.)
b^2 = 20,736 (Now take the square root.)
b = 144
Your answer should be:
AB = 144