Ab is tangent to circle o. if ao = 17 and bc = 128, what is ab?

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