#### Answer

Chord AB is about 1.27 inches closer.

#### Work Step by Step

Let x represent the distance from chord AB to point P. Let y represent the distance from chord CD to point P.
The perpendicular bisector from chord AB to point P splits triangle APB into two 45 45 90 triangles with radii for hypotenuses. Therefore:
x=$\frac{8}{\sqrt 2}$
x=4$\sqrt 2$
The perpendicular bisector from chord CD to point B splits triangle CPD into to 30 60 90 triangles with radii for hypotenuses. Therefore:
y=$\frac{8}{2}$($\sqrt 3$)
y=4$\sqrt 3$
y-x=4$\sqrt 3$-4$\sqrt 2$$\approx$1.27