For the circle centered at X, as illustrated:
Draw a diameter that runs parallel to chord AB, as depicted in the figure.
Given that the diameter and AB are parallel, the line segment XC, which intersects AB at midpoint C, will be at a right angle to AB.
Thus, triangle XCB forms a right triangle. Consequently, using the Pythagorean theorem, the length of CX is

units.
The answer is: 8 units