Answer:
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
