## Elementary Geometry for College Students (6th Edition)

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