Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 6 - Section 6.4 - Some Constructions and Inequalities for the Circle - Exercises - Page 302: 31

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
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