Ab is tangent to circle o. if ao=16 and bc=18 what is ab

AB = 30 units

Step-by-step explanation:

For a better understanding of the answer see the figure of the problem attached

By using the property that the tangent make right angle with the radius of the circle.

We get, ∠OAB = 90°.

AO = 16 units  ⇒ CO = 16 units  (radius of the same circle)

BC = 18 units.

So, OB = BC + CO

      OB = 16 + 18 = 34 units

So, In ΔAOB using Pythagoras theorem :

OB² = AO² + AB²

34² = 16² + AB²

⇒ AB² = 34² - 16²

⇒ AB² = 1156 - 256

⇒ AB² = 900

⇒ AB = 30 units