The diagram shows a circle, centre O - Edexcel - GCSE Maths - Question 22 - 2019 - Paper 3

First, since angle OBA = 30°, we can use trigonometric ratios to find the distances involved:

Since AB is tangent to the circle, we know the radius at point A is perpendicular to AB, thus triangle OBA is a right triangle. The length of OA can be calculated as follows:

1. The distance from O (the center of the circle) to B (16, 0) is equal to the radius, which is 6.

Using the relationship in triangle OBA:

$\tan(30^{\circ}) = \frac{OA}{AB}$

Since OA = 6, we can calculate the length of AB:

$AB = \frac{OA}{\tan(30^{\circ})} = \frac{6}{\frac{1}{\sqrt{3}}} = 6\sqrt{3}$